Involute splines
A DIN 5480 W 40 x 2 x 18 spline is named by its reference diameter: 18 teeth of module 2 on a 36.000 mm pitch circle, shifted x = 0.45 so the shaft’s tip is 39.600 mm and the hub’s root 40.000 mm. Enter a DIN 5480 or ISO 4156 designation for the basic sizes and the measurement over pins on the shaft or between pins in the hub.
The shaft is drawn in its hub in end view, or on its own between the pins a micrometer reads over.
DIN 5480 – W 40 x 2 x 18 x 8f: the shaft, 18 teeth, module 2, 30°, tolerance 8f, flank-centred.
- Pitch Ø d
- Reference Ø dB
- Profile shift x
- Base Ø db
- Tooth thickness = space width on d
- Shaft tip Ø da₁
- Shaft root Ø df₁
- Hub tip Ø da₂
- Hub root Ø df₂
- Over pins M (shaft), Ø4.369
- Between pins M (hub), Ø3.702
How it’s calculated
For DIN 5480 the shaft’s tip is dB − 0.2·m and the hub’s dB − 2·m; the roots are d + 2x·m ∓ 2hfP, with hfP 0.55·m broached, 0.60·m hobbed, 0.65·m shaped and 0.84·m cold rolled. ISO 4156 has no shift (x = 0, s = πm/2); its major and minor diameters are m·(z ± a constant) for the pressure angle and root. Over pins: inv φ = dp/(m·z·cos α) − π/2z + inv α + 2x·tan α/z and M = db/cos φ + dp on an even count; between pins in the hub, inv φ = π/2z + inv α − dp/(m·z·cos α) + 2x·tan α/z and M = db/cos φ − dp. Here: d = 2 × 18 = 36.000 mm, x = 0.4500, and M over Ø4.369 pins = 44.800 mm.
How do DIN 5480 and ISO 4156 splines differ?
Both are involute splines, usually 30° and centred on their flanks, but they are sized differently. DIN 5480 names a spline by its reference diameter, close to the shaft’s outside diameter, and shifts the tooth profile so a round-number size fits any module: W 40 x 2 x 18 is a 40 mm shaft. ISO 4156 names it by tooth count and module and does not shift the profile, so the pitch diameter is m·z and the outside diameter is seldom a round number; it adds 37.5° and 45° forms for finer, stronger teeth. The two do not mate.