Keys and splines

What it is for

The Keys module checks shaft–hub connections that transmit torque by form: a parallel (feather) key in a keyway, or an involute spline. For a key it picks the DIN 6885-1 key and keyway for the shaft diameter and checks the flank pressure on shaft, hub and key after DIN 6892, on the heights the key bears in the shaft groove and in the hub. For a spline it checks the flank pressure and the tooth shear, and for DIN 5480 it also gives the inspection dimensions. Each joint is a stand-alone case. The keyway as a notch in the shaft is assessed separately, in the shaft strength check.

Inputs

Open Keys and choose + Key or + Spline (on the empty page: Add a key or Add a spline). The inspector shows these groups.

Connection

Type: Parallel key (DIN 6885 / 6892) or Involute spline.

For a parallel key:

Shaft diameter (mm): selects the DIN 6885-1 key b × h and the keyway depths t1 (shaft) and t2 (hub). The table covers shafts of 6–500 mm.
Hub length (mm): the key length l.
Key form: A, round ends (bearing length l − b) or B, square ends (bearing length l).
Keys: One or Two at 180°. Two keys are taken to share the load with φ = 0.75, so the pair carries 1.5 times one key, not twice.
Key width b and Key height h (mm): leave empty ("DIN 6885") to use the standard key for the diameter. Give them only for a special key.
Shaft depth t1 (shaftDepth, mm): the depth of the shaft groove, measured from the shaft's circle on the keyway's centre line (as DIN 6885-1 dimensions it, d − t1); empty takes the DIN 6885-1 depth. A deeper groove leaves less of the key in the hub, a shallower one less in the shaft, and the flank pressure follows (see below). A depth that leaves the key no flank in the shaft or the hub is refused, with the depth to use.

For a spline:

Standard: DIN 5480 or ISO 4156.
Pressure angle: 30°, 37.5° or 45° for ISO 4156. DIN 5480 is always 30°, so the field is locked.
Module m (mm) and Teeth z.
Engaged length (mm): the length over which hub and shaft teeth overlap.
Reference diameter dB (mm, DIN 5480 only): the d_B in the designation W d_B × m × z. Empty means $m \cdot (z + 1.1)$ , that is no profile shift. DIN 5480 allows profile shift factors from −0.05 to +0.45.
Pin diameter, shaft and Pin diameter, hub (mm, DIN 5480 only): the measuring pins for the dimensions over and between pins; empty means 2·m and 1.75·m.

Load

Torque (N·m): the nominal torque.
Application factor KA: for torque peaks from the driving and driven machines (1 for a smooth drive; the template uses 1.25).
Load peak factor Kλ: the uneven torque distribution along the joint. Empty ("estimated") takes an approximation of DIN 6892 Fig. 5: 1 up to a bearing length equal to the diameter, then +0.4 per further diameter.
Support factor fS (default 1.2): the flank pressure on shaft and hub is checked against fS·Re. Use 1.2 for ductile steel; 1.5–2.0 is typical for grey cast iron hubs. The key itself is always checked against Re.

Materials

Shaft, Hub and, for a key, Key. Each list offers S235, S355, C45 +C, C45 +QT, 42CrMo4 +QT, 16MnCr5 case hardened, Ductile iron GJS-400 and Grey iron GJL-250 (Rm), each with its yield strength Re. C45 +C (Re 430 MPa) is a usual key steel.

Requirements

Min safety (default 1): the same limit for every flank and the tooth shear. Clear it ("none") to switch the check off.

Results

The right pane shows the checks and two key figures: Flank pressure (at KA·T) and Torque capacity (the nominal torque at which the lowest safety reaches 1). The centre shows a Cross-section of the joint and the cards Factors (Kλ, load share φ, permissible pressures), DIN 6885-1 (key) or DIN 5480 dimensions (spline).

In 3D the shaft, the hub (cut away over a quarter) and the key or the spline teeth are drawn at their real sizes, coloured by the flank pressure over the permissible one; the pressure peaks at the end where the torque comes in, by the load peak factor Kλ. Hovering turns the joint half a turn. The 2D and 3D tabs above the drawing switch to a 3D model; the choice is kept for the module. In 3D, drag to orbit and scroll to zoom; the model stands still and plays its motion once when the pointer moves onto it or it gets the keyboard focus (never with reduced motion). Without WebGL the drawing stays, with a note.

The Keyed hub and splined shaft template has a parallel key on Ø40 mm (form A, 50 mm hub, C45 +QT shaft, S355 hub, C45 +C key) and a spline W 40 × 2 × 18, 40 mm engaged, both at 300 N·m with KA 1.25:

Result	Key K1	Spline K2
Geometry	key 12 × 8, t1 5.0, t2 3.3 mm	x·m 0.9 mm, mean diameter 37.8 mm
Bearing length, flank height	38 mm; 3.479 mm shaft, 3.321 mm hub	40 mm, 1.8 mm
Kλ, load share	1.0, 1.0	1.023, 0.75
Flank pressure at 375 N·m	141.8 MPa shaft, 148.6 MPa hub	20.89 MPa
Permissible shaft / hub	588 / 426 MPa	588 / 426 MPa
Safety shaft / hub	4.146 / 2.867	28.15 / 20.39
Safety key or tooth shear	2.894 (key, Re 430 MPa)	21.71 (τ 9.443 MPa)
Torque capacity	860.2 N·m	6118 N·m

What each result means

Flank pressure, key: $p = \frac{2 \cdot T \cdot K_{A} \cdot K_{λ}}{d \cdot h^{'} \cdot l_{t r} \cdot i \cdot φ}$ as in DIN 6892, with the bearing length l_tr (l − b for form A, l for form B), the number of keys i and the load share φ, on each side with the height h′ the key bears there. The groove depth t1 is measured from the shaft's circle on the keyway's centre line; at the key's flanks, b/2 off that line, the circle of shaft and hub bore lies lower by the chord height $c = d / 2 - \sqrt{d^{2} / 4 - b^{2} / 4}$ . The key therefore bears $h^{'} = t_{1} - c - s$ in the shaft and $h^{'} = h - t_{1} + c - s$ in the hub, s being the key's edge chamfer r1 at its largest (DIN 6885-1). For the template: c = 20 − √(400 − 36) = 0.921 mm, so 5 − 0.921 − 0.6 = 3.479 mm in the shaft and 8 − 5 + 0.921 − 0.6 = 3.321 mm in the hub, and on the hub 2·375 000/(40·3.321·38) = 148.6 MPa. The key carries the higher of the two pressures. For the DIN 6885-1 keyways these heights are about half the key less its chamfer, within some 15 % of the $h^{'} = 0.45 \cdot h$ of DIN 6892's simplified method C (lower for the small 2 × 2 key); for a groove deeper or shallower than the standard's they follow the depth entered, which the 0.45·h approximation cannot.
Flank pressure, spline: the same idea on the mean flank diameter, $d_{B} - 1.1 \cdot m$ for DIN 5480 (m·z for ISO 4156), with a flank overlap of 0.9·m, 0.8·m or 0.7·m for 30°, 37.5° or 45° and 75 % of the teeth carrying.
Safeties: permissible pressure over the pressure, for shaft (fS·Re over the shaft's pressure), hub (fS·Re over the hub's) and key (Re over the higher). In the template the hub is the weak part: 1.2 × 355 = 426 MPa.
Tooth shear (splines): the shear stress at the pitch circle against $R_{e} / \sqrt{3}$ of the weaker of shaft and hub.
DIN 6885-1 card: keyway depths t1 / t2 with their tolerance (+0.2 mm here), the hub depth for a key with interference (2.4 mm), chamfer and root radius, the length tolerance and whether the length is in the standard range (28–140 mm for this key).
DIN 5480 dimensions card: profile shift x·m and tooth thickness, tip, root and form diameters of shaft and hub, dimension over pins M1 and between pins M2, and the base tangent length W_k. For the template spline: shaft tip 39.6 mm, shaft root 35.6 mm, M1 43.846 mm over Ø4 pins, M2 32.739 mm between Ø3.5 pins, W4 21.621 mm.

Fixing a failing check

Hub flank: a stronger hub material or a longer hub. For a grey cast iron hub, use the support factor its material justifies (1.5–2.0 is typical) rather than the steel value. A longer hub helps fully only up to about one diameter of bearing length, because Kλ then rises.
Key flank: a stronger key steel, form B for more bearing length, or two keys at 180°.
Shaft flank: a stronger shaft material or a larger diameter (which also gives a larger key). A shallow custom groove (small t1) bears little in the shaft: use the DIN 6885-1 depth.
Hub flank with a deep groove: a groove deeper than the DIN 6885-1 depth leaves little of the key in the hub; use the standard depth or a taller key.
If a key will not fit the torque, use a spline: the template spline carries more than six times the key's capacity on the same diameter.
Check KA honestly: it multiplies the pressure directly.

Standards and scope

Parallel keys after DIN 6892 (flank pressure on the heights the key bears in shaft and hub, from the keyway geometry), key and keyway dimensions after DIN 6885-1:1968 (form A and B).
DIN 5480 geometry from the reference profile of DIN 5480-1:2006 (form diameters after Tables 3 and 4) and the inspection dimensions computed from the involute as tabulated in DIN 5480-2:2006. axm verify checks these dimensions and the DIN 6885-1 key rows against the printed tables ("Splines and keys: DIN 5480 and DIN 6885-1 dimensions", 43 checks).
ISO 4156 splines are rated for flank pressure and shear; the dimensions card is computed for DIN 5480 only.
Static checks at the peak torque KA·T only. Fretting, wear and fatigue under reversing torque are not assessed. DIN 6892 method A, the shaft strength proof of DIN 6892 method B (the keyway as a notch is in the shaft strength check), taper keys, Woodruff keys and polygon profiles are not included.

From the command line

axm new drive.axm.json --template keyed-joints
axm solve drive.axm.json
axm key add drive.axm.json --name "Coupling key" --patch '{"diameter":55,"length":70,"torque":800,"applicationFactor":1.5}' --json

axm guide keys lists every field with its unit and default.

Open the Keyed hub and splined shaft example
Fits and press fits
Bolted joints
Shaft strength for the keyway as a notch
ISO 286 and DIN 7190 press fits