KEVOS® MAKEOS · Power Transmission
Involute Spline Design Check (Proportions, Root and Tooth Stresses)
For this inch involute spline, what are its diameters and tooth proportions, and are the shear and compressive stresses within limits for my torque and engagement length?
Check of a side-fit or major-diameter-fit involute spline: pitch, major, minor, root and form diameters and the basic tooth thickness for the diametral pitch, tooth count and type (as the involute spline tool), the depth of engagement from the external major and internal minor diameters, then the shear stress under the roots, the shear at the pitch diameter and the tooth compressive stress with application, load-distribution, fatigue and wear factors (as the spline torque capacity tool), against the allowable shear and compressive stresses.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Diametral pitch P (e.g. 16 for 16/32) | 1/in | Diametral pitch of the spline (the first number of the pitch fraction). |
| Number of teeth | teeth | Number of teeth. |
| Spline type | choice | Root form and fit. |
| Load | ||
| Transmitted torque | N·m | Torque transmitted. |
| Effective length | mm | Length of the spline engagement. |
| Bore of a hollow shaft (0 = solid) | mm | Bore of a hollow shaft. |
| Spline | choice | Fixed splines do not slide; flexible ones allow misalignment or sliding. |
| Spacing accuracy | choice | Spacing accuracy of the teeth. |
| Application factor | Application factor for the driver and load. | |
| Load distribution factor | Load distribution factor for misalignment. | |
| Fatigue life factor | Fatigue life factor. | |
| Wear life factor (flexible) | Wear life factor for flexible splines. | |
| Allowable shear stress | MPa | Allowable shear stress of the shaft and teeth. |
| Allowable compressive stress | MPa | Allowable compressive (bearing) stress on the teeth. |
Method and formulas
- Pitch diameter D = N ÷ P; external major, internal minor and root diameters and the basic tooth thickness π ÷ 2P for the type (as the involute spline tool), converted to millimetres.
- Depth of engagement h = (external major − internal minor) ÷ 2.
- Root shear = 16 T K_a ÷ (π D_re³ K_f); pitch shear = 4 T K_a K_m ÷ (D N L_e t K_f); compressive = 2 T K_m K_a ÷ (9 D N L_e h K_f) for fixed splines (as the spline torque capacity tool).
- Example: D = 31.75 mm, root 29.607 mm; root shear 70.647 MPa and tooth compression 3.1744 MPa.
Limitations
- Dudley spline formulas with the factors you enter.
- Basic dimensions; tolerances and fit classes come from the standard.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check a spline for a new torque
- Choose spline length for a hub
- Get spline diameters for a drawing
Who it is for
- Design engineers
- Gear and spline designers
- Machine designers
What you get
- Pitch, major, minor and root diameters
- Tooth thickness and depth of engagement
- Root shear, pitch shear and compressive stress
Interpreting the result
- Lengthening a spline beyond about one pitch diameter adds little capacity because load concentrates at one end.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2255–2282. Topic reference; no source tables or recommended settings are reproduced.
- ANSI B92.1 Involute Splines and Inspection
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Open the Involute Spline Design Check (Proportions, Root and Tooth Stresses) calculator
