KEVOS® MAKEOS · Gears
Spline Joint Design (Engagement Length and Stresses)
How long must this involute spline engage to carry the torque, and are the shaft and teeth within their allowable stresses?
Design of a metric-module involute spline joint (30° flat-root proportions): pitch, minor diameter, tooth thickness and working depth from module and tooth count, root shear stress of the shaft, the engagement length needed for tooth shear at the pitch line and for tooth compression (fixed or flexible spline), and the stresses at the length chosen, by the same method as the spline torque capacity tool.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Torque | N·m | Torque the joint transmits. |
| Module | mm | Module of the spline (pitch diameter ÷ teeth). |
| Number of teeth | Number of spline teeth. | |
| Engagement length | mm | Length over which the teeth of shaft and hub engage. |
| Bore of a hollow shaft (0 = solid) | mm | Bore diameter if the shaft is hollow. |
| Spline type | choice | A fixed spline does not slide; a flexible spline slides or accepts misalignment and is limited by wear. |
| Spacing accuracy | choice | Accuracy of tooth spacing, which sets how many teeth share the load. |
| Application factor | Application factor for shock in the drive. | |
| Load distribution factor | Load distribution factor for misalignment along the length. | |
| Fatigue life factor | Fatigue life factor for the number of torque cycles. | |
| Wear life factor (flexible splines) | Wear life factor for flexible splines. | |
| Allowable shear stress | MPa | Allowable shear stress of the spline material (your design value). |
| Allowable compressive stress | MPa | Allowable compressive stress on the tooth flanks (your design value). |
Method and formulas
- Pitch diameter D = m N; external minor diameter D_re = m (N − 1.35); tooth thickness t = π m ÷ 2; working depth h = m (30° flat-root proportions).
- Root shear S_s = 16 T K_a ÷ (π D_re³ K_f) for a solid shaft (hollow: 16 T D_re K_a ÷ [π (D_re⁴ − D_h⁴) K_f]).
- Tooth shear at the pitch line S = k T K_a K_m ÷ (D N L t K_f), k = 4 (good spacing) or 6; compressive S_c = 2 T K_m K_a ÷ (9 D N L h K_f) fixed, or 2 T K_m K_a ÷ (D N L h K_w) flexible.
- Length needed = the larger of the lengths that bring tooth shear and compression to their allowables.
- Example: 500 N·m on a 20-tooth module 2 spline needs 4.7746 mm of engagement; the root shear stress is 58.884 MPa.
Limitations
- Simplified method; full spline rating uses the standard’s factors and tooth geometry.
- Flat-root proportions; fillet-root splines have a slightly larger minor diameter.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Size the engagement length of a splined hub
- Check a splined shaft end for a torque increase
- Compare fixed and flexible (sliding) splines
Who it is for
- Design engineers
- Maintenance engineers
- Power transmission engineers
What you get
- Spline proportions from module and teeth
- Root shear stress
- Engagement length needed and stresses at the length chosen
Interpreting the result
- Engagement beyond about one pitch diameter adds little: misalignment concentrates the load 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; ISO 4156 Straight cylindrical involute splines
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Open the Spline Joint Design (Engagement Length and Stresses) calculator
