BIZOMAT 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. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Diametral pitch P (e.g. 16 for 16/32)
- What it is
- The diametral pitch of the spline: teeth per inch of pitch diameter, the first number of the pitch fraction.
- Units and format
- Enter a number in 1/in: threads per inch. The form accepts 0.000001 1/in to 128 1/in. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 16 1/in as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter the first number only; the second number (the stub pitch) is not used by the tool.
What this means: Number of teeth
- What it is
- The number of teeth on the spline; with the diametral pitch it sets the pitch diameter.
- Units and format
- Enter a number in teeth: a whole number of teeth. The form accepts 6 teeth to 100 teeth. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 teeth as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Spline type
- What it is
- The root form and fit of the spline, which set the major, minor and root diameters and the basic tooth thickness.
- Units and format
- Choose one of 4 options from the list: 30° flat root, side fit; 30° flat root, major diameter fit; 30° fillet root, side fit; 37.5° fillet root, side fit.
- Example
- The form opens with “30° flat root, side fit” selected as a worked example. Choose the option that matches your case.
Load
What this means: Transmitted torque
- What it is
- The torque transmitted through the spline connection.
- Units and format
- Enter a number in N·m: newton-metres. The form accepts 0.000001 N·m to 100000000 N·m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 300 N·m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Every stress the tool reports rises in proportion to torque.
What this means: Effective length
- What it is
- The axial length over which the external and internal spline teeth engage.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 25 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Pitch shear and tooth compressive stress fall in proportion to length; root shear does not change.
What this means: Bore of a hollow shaft (0 = solid)
- What it is
- The bore of a hollow externally splined shaft; zero means a solid shaft.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Only the root shear stress uses it, and it must be smaller than the external root diameter.
What this means: Spline
- What it is
- Whether the spline is fixed (no sliding) or flexible (allows misalignment or sliding); it changes the tooth compressive stress formula.
- Units and format
- Choose one of 2 options from the list: Fixed; Flexible.
- Example
- The form opens with “Fixed” selected as a worked example. Choose the option that matches your case.
What this means: Spacing accuracy
- What it is
- The spacing accuracy of the teeth, which sets how many teeth are taken to share the load in the pitch shear stress.
- Units and format
- Choose one of 2 options from the list: Normal accuracy (half the teeth carry load); Lower accuracy (a third of the teeth).
- Example
- The form opens with “Normal accuracy (half the teeth carry load)” selected as a worked example. Choose the option that matches your case.
What this means: Application factor
- What it is
- A multiplier on torque for the type of driver and driven load, from a spline or gear design reference.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 4. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.2 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Load distribution factor
- What it is
- A multiplier for uneven load along the teeth caused by misalignment, from a spline design reference.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 4. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Fatigue life factor
- What it is
- A factor for the number of load cycles in the required life; the stresses are divided by it, so a lower value is more conservative.
- Units and format
- Enter a plain number with no unit. The form accepts 0.1 to 2. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- For a flexible spline the compressive stress uses the wear life factor instead of this one.
What this means: Wear life factor (flexible)
- What it is
- A wear life factor used only for flexible splines in the tooth compressive stress; the stress is divided by it.
- Units and format
- Enter a plain number with no unit. The form accepts 0.1 to 2. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Ignored for fixed splines, which use the fatigue life factor instead.
What this means: Allowable shear stress
- What it is
- The allowable shear stress of the shaft and teeth, compared with the larger of the root shear and pitch shear stresses.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 5000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 200 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Allowable compressive stress
- What it is
- The allowable compressive (bearing) stress on the tooth flanks, from a spline design reference for the material and hardness.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 5000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
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