KEVOS® MAKEOS · Power Transmission
Involute Spline Stresses and Torque Capacity
Are the shear and compressive stresses in this involute spline within the allowables for the torque?
Stresses in a 30° involute spline by the handbook (Dudley) formulas: shear under the roots of the external teeth for a solid or hollow shaft, shear at the pitch diameter, and compressive stress on the tooth sides for fixed or flexible splines, using application, load-distribution, fatigue-life and wear-life factors.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Transmitted torque | N·m | Torque through the spline. |
| Pitch diameter | mm | Pitch diameter. |
| Root diameter of the external spline | mm | Root (minor) diameter of the external spline. |
| Bore of a hollow shaft (0 = solid) | mm | Inside diameter of a hollow shaft. |
| Number of teeth | Number of spline teeth. | |
| Effective length | mm | Effective length carrying load (limited by misalignment; never more than the engaged length). |
| Circular tooth thickness at the pitch diameter | mm | Circular tooth thickness at the pitch diameter. |
| Depth of engagement | mm | Radial depth of tooth engagement (about 0.9 module for flat root, 1 module for fillet root). |
| Spline | choice | A fixed spline is piloted or shrunk on so it cannot rock; a flexible spline rocks and wears. |
| Spacing accuracy | choice | Spacing accuracy of manufacture. |
| Application factor | Application factor for the power source and load. | |
| Load distribution factor (1 for fixed) | Load distribution factor for misalignment (1 for fixed splines). | |
| Fatigue-life factor | Fatigue-life factor for the number of torque cycles. | |
| Wear-life factor (flexible) | Wear-life factor for the revolutions of a flexible spline. | |
| Allowable shear stress | MPa | Allowable shear stress for your material and hardness. |
| Allowable compressive stress | MPa | Allowable compressive stress for your material and spline type. |
Method and formulas
- Root shear, solid: S_s = 16 T K_a ÷ (π D_re³ K_f); hollow: 16 T D_re K_a ÷ [π (D_re⁴ − D_h⁴) K_f].
- Pitch-line shear: S_s = 4 T K_a K_m ÷ (D N L_e t K_f), with 6 in place of 4 for poor spacing accuracy.
- Compression, flexible: S_c = 2 T K_m K_a ÷ (D N L_e h K_w); fixed: 2 T K_m K_a ÷ (9 D N L_e h K_f).
- Example: 500 N·m in a 24-tooth spline gives 139.2 MPa root shear.
Limitations
- 30° involute splines; bursting of internal splines is a separate check.
- Factors and allowables are user inputs from the spline standard and material data.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check a spline for a new torque or duty
- Find the effective length a spline needs
- Compare fixed and flexible spline designs
Who it is for
- Design engineers
- Gear designers
- Driveline engineers
What you get
- Shear stress under the roots
- Shear stress at the pitch diameter
- Compressive stress on the teeth
Interpreting the result
- If compression governs, lengthen the engagement or make the spline fixed (piloted).
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2266–2270. Topic reference; no source tables or recommended settings are reproduced.
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