DIN 5480 splines (30°, flank-centred) from the designation W dB × m × z: profile shift, tip and root diameters of shaft and hub, base diameter and tooth thickness. Then the load check: flank pressure, the engagement length a torque needs, torque capacity, shaft torsion at the root and hub hoop stress, for fixed and sliding fits. ANSI B92.1 flat-root side-fit splines too.
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Reference diameters 6 – 120 mm against module. Each cell is the tooth count that keeps the profile shift inside the DIN 5480 range x = −0.05 … +0.45 (even z where two counts fit, as in the DIN 5480-2 tables). Click a cell to use that size. DIN 5480-2 lists the sizes it standardises; check availability of broaches and hobs for unusual combinations.
DIN 5480 splines are named by the reference diameter dB, which is close to the shaft outside diameter, not by the pitch diameter. All splines use one 30° basic rack with addendum 0.45·m and dedendum 0.55·m. The profile shift x·m makes the teeth fit the chosen dB, and the tooth count is picked so that x stays between −0.05 and +0.45. Hub and shaft are centred on the flanks; the tips clear the roots by 0.1·m.
This is the simplified mean-pressure check used in Roloff/Matek, Decker and Niemann for a first design: the torque is shared by three quarters of the teeth with a uniform pressure over the bearing height and the credited length. The full method of DIN 5466-1 replaces φ and the length cap by circumferential and face load-distribution factors (kφ, kβ) from the torsional and bending stiffness of shaft and hub, checks the tooth root and the shaft notch for fatigue, and handles bending moments and reversing torque. Use that method, or test data, for highly loaded, reversing or long splines. Shaft fatigue at the spline run-out is checked separately in the shaft calculator (Kt for splines about 2.5 – 3 in torsion).
The tip and root diameters are nominal values for the basic profile. Real hubs are broached or shaped and real shafts are hobbed, shaped or cold rolled, and the tool, the tolerance class (for example 9H / 8f) and the deviation series move the root diameters by a few hundredths of a millimetre; DIN 5480-2 gives the inspection dimensions over pins and over k teeth for each size.
This calculator works out an involute spline to DIN 5480 from its designation W dB × m × z, or an ANSI B92.1 flat-root side-fit spline from teeth and pitch. Enter the reference diameter and module (or pick a size from the chart), the torque with an application factor, the engaged length and the hub outside diameter, and choose the fit and materials. It returns the profile shift, the tip and root diameters of shaft and hub, the base diameter and tooth thickness, then the flank pressure, the engagement length the torque needs, the torque capacity, shaft torsion at the root and the hub hoop stress, with a table comparing the modules available at your diameter.
The W 40×2×18 spline carries 1000 N·m with shocks at a quarter of the allowable flank pressure; the shaft cross-section at the tooth roots (56 %) is the real limit, which is typical for splines. A 10 mm engagement would satisfy the flanks, but a length near 1·dB is advisable for guidance and wear.
W stands for shaft (Welle), N for hub (Nabe). 40 is the reference diameter dB in mm, close to the shaft outside diameter; 2 is the module in mm and 18 the number of teeth. A full designation adds the tolerance class and deviation, for example DIN 5480 – W 40×2×18×8f for the shaft and N 40×2×18×9H for the hub.
DIN 5480 fixes the reference diameter and the module and adapts the teeth with a profile shift x·m = (dB − m·z − 1.1·m)/2. The tooth count is chosen so that x stays between −0.05 and +0.45; when two counts fit, the standard tables use the even one, for example W 40×2×18 rather than 19 and W 50×2×24 rather than 23.
The simplified method assumes a uniform pressure on the flanks: p = 2·T·KA / (dm · h' · L · z · φ). For DIN 5480 the mean diameter is dm = dB − 1.1·m and the bearing height h' = 0.9·m; the load-share factor φ ≈ 0.75 accounts for pitch errors so that not every tooth carries. The torque capacity follows by setting p to the allowable pressure of the weaker part.
Much lower than for a fixed one, because wear rather than strength decides. SAE and ANSI B92.1 give about 1500 psi (10 MPa) for soft steel, 2000 – 3000 psi for through-hardened and up to 5000 psi (35 MPa) for case-hardened flanks of splines that slide under load, against roughly 0.9 × yield for a fixed spline. Crowned teeth and good lubrication raise the limit.
Long enough for the flank pressure, but beyond about 1.3 times the reference diameter the shaft twists along the spline and the far end carries little, so extra length does not add capacity. Lengths around 0.8 – 1.3 × dB are common; for higher torque use a larger diameter or harder flanks.
DIN 5466-1 is the detailed load capacity method for splines: it uses circumferential and face load-distribution factors from the stiffness of shaft and hub, checks the tooth root and shaft notch for fatigue and handles bending and reversing loads. The mean-pressure check here is the quick design method of Roloff/Matek and Niemann and is good for sizing, not for final proof of highly loaded splines.
What you need to build, measure or check the result.
Gear tooth vernier caliperCheck tooth thickness on the splineView on Amazon →
Gauge pin setMeasure over pins for spline sizeView on Amazon →
Anti-seize assembly pasteProtect sliding splines from frettingView on Amazon →As an Amazon Associate TorqueMath earns from qualifying purchases. Prices and availability are shown on Amazon.
Checked: 6 results compared with textbooks, standards and maker data by a separate review, 3 corrections made. See the checks →