Splined Shaft Connection Calculator (DIN 5480)
Verify involute splined shaft connections per DIN 5480: from the reference diameter, module, load-carrying length and operating torque follow the number of teeth, mean load-carrying diameter, flank pressure and transmittable torque with a safety factor against the hub.
Calculation
DIN 5480: z = 24, d_m = 48 mm, h_tr = 0.9 mm
- Equivalent torque T_eq = K_A · T
- 1,000 Nm
- Transmittable torque T_allow
- 3,541.1 Nm
- Mean load-carrying diameter d_m
- 48 mm
- Load-carrying tooth height h_tr
- 0.9 mm
Simplified flank pressure verification per Niemann/Roloff-Matek, not an exact calculation per DIN 5480-1 (no tolerance class, no friction or wear analysis).
Root load capacity and the notch effect of the spline on the shaft are not covered here - use the DIN 743 shaft calculator for that.
DIN 5480 describes the involute spline; the older straight-sided spline per DIN ISO 14 is a separate connection type with a higher notch effect.
Cross-section: splined shaft profile with hub
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Formulas and fundamentals
Geometry per DIN 5480
The splined shaft connection per DIN 5480 is an involute spline with many, evenly distributed teeth: the number of teeth follows from the reference diameter d_B and the module m using the DIN 5480 convention. If the result is not an integer, it is conservatively rounded up with a note - the chosen combination of d_B and m then does not correspond to a regular DIN 5480 size.
The mean load-carrying diameter and the load-carrying tooth height (guideline value for involute splines) follow as:
Equivalent torque and flank pressure
The operating torque is increased by the application factor to the equivalent torque and converted via the mean load-carrying diameter into a circumferential force, which is distributed over the load-carrying length, all z teeth and the load-sharing factor φ:
The load-sharing factor φ (default 0.75, range 0.5 to 0.8) accounts for the fact that manufacturing tolerances prevent a perfectly even load distribution across all teeth - similar to the load-sharing factor of a second parallel key.
Allowable flank pressure and safety factor
The flank pressure is allowable up to a value that depends on the hub's yield strength, its heat treatment and the required safety factor:
Here f_H is the hardness factor: f_H = 1.0 for quenched-and-tempered hubs, f_H = 1.5 for case-hardened hubs, which withstand a considerably higher flank pressure thanks to the hard surface layer. The safety factor S_F defaults to 1.3. The utilization is:
Transmittable torque
Rearranging the pressure formula for torque gives the nominal torque transmittable at the given geometry and safety factor - directly comparable to the operating torque T:
Worked example
Given: splined shaft connection per DIN 5480 with reference diameter d_B = 50 mm and module m = 2 mm (giving z = 24), load-carrying length l_tr = 40 mm, operating torque T = 800 Nm with application factor K_A = 1.25 (light shocks). Hub of quenched-and-tempered C45 (R_e = 370 N/mm²), load-sharing factor φ = 0.75 and safety factor S_F = 1.3 (both defaults).
Calculation: d_m = 50 - 2 = 48 mm, h_tr = 0.45 · 2 = 0.9 mm, T_eq = 1.25 · 800 = 1000 Nm = 1,000,000 Nmm. Flank pressure p = 2 · 1,000,000 / (48 · 0.9 · 40 · 24 · 0.75) = 64.3 N/mm².
Verification: p_allow = 370 · 1.0 / 1.3 = 284.6 N/mm². Utilization = 64.3 / 284.6 = 0.226 (23%, pass, green rating). Transmittable torque T_allow = 284.6 · 48 · 0.9 · 40 · 24 · 0.75 / (2000 · 1.25) = 3541 Nm - well above the required 800 Nm.
Frequently asked questions
What is the difference between a splined shaft connection and a parallel key connection?
The splined shaft connection per DIN 5480 transmits torque through many evenly distributed teeth instead of a single parallel key. This gives the shaft a much lower notch effect, results in a low-backlash connection, and allows high alternating or shock torques as well as axially sliding hubs (sliding fit). The drawback is higher manufacturing cost compared to a simple keyway.
How much torque can a DIN 5480 splined shaft transmit?
The transmittable torque T_allow follows from the allowable flank pressure, the geometry (mean load-carrying diameter, load-carrying tooth height, number of teeth, load-carrying length) and the load-sharing factor φ. For the example W 50 × 2 × 24 with l_tr = 40 mm and a quenched-and-tempered C45 hub, T_allow ≈ 3541 Nm - the calculator outputs this value directly for any input.
What is the load-sharing factor φ in a splined shaft connection?
Manufacturing tolerances prevent all teeth of a splined shaft connection from carrying load perfectly evenly - some teeth take on more load than others. The load-sharing factor φ (default 0.75, typical range 0.5 to 0.8) accounts for this by reducing the theoretically available load-carrying area accordingly. A smaller value should be used for larger pitch deviation or a lower tooth count.
What do reference diameter, module and number of teeth mean in DIN 5480?
The reference diameter d_B is the spline's reference dimension, the module m determines the tooth size - together, via the DIN 5480 convention z = d_B/m - 1, they fix the number of teeth. A splined shaft W 50 × 2 × 24 therefore has d_B = 50 mm, m = 2 mm and z = 24 teeth. If a chosen combination does not give an integer tooth count, the calculator flags it and conservatively rounds up.
When should the hub be case-hardened instead of quenched-and-tempered?
Case-hardened hubs (e.g. of 16MnCr5) withstand a considerably higher flank pressure than quenched-and-tempered hubs thanks to the hard, wear-resistant surface layer - the calculator applies a flat hardness factor f_H = 1.5 for this. It pays off for highly utilized connections, sliding fits subject to wear, or whenever a quenched-and-tempered hub would exceed the allowable pressure.
How does DIN 5480 differ from the involute-free spline per DIN ISO 14?
DIN 5480 describes an involute spline with many, flat teeth and a low notch effect - the standard for highly loaded, low-backlash shaft-hub connections in mechanical engineering. The straight-sided spline per DIN ISO 14 (formerly DIN 5471/5472) instead has only a few straight driving splines with a considerably higher notch effect, and today is mainly used for simpler, lower-load applications or in legacy designs.