KEVOS® MAKEOS · Manufacturing
Spline Shaft Milling Cutter (Cutter Angle and Chordal Width at the Root)
To mill a straight-sided splined shaft with a formed cutter, what included angle must the cutter have and what chordal width must its concave edge have so that it cuts the space between two splines down to the root diameter?
Proportions of a special milling cutter that forms the space between adjacent splines of a straight-sided splined shaft, by the handbook formulas: the cutter angle B = 360° ÷ N, the angle A between the centre line of a spline and a radial line through the point where its side meets the root circle (sin A = W ÷ d), and the chordal width C = d sin(180° ÷ N − A) at the root circle between adjacent splines, which is the chordal width across the concave edge of the cutter.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Number of splines | splines | Number of splines around the shaft. |
| Width of each spline | mm | Width of each spline across its parallel sides. |
| Root (minor) diameter of the splined shaft | mm | Root diameter of the splined shaft, where the cutter forms the bottom of each space. |
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: Number of splines
- What it is
- Number of straight-sided splines around the shaft to be milled.
- Units and format
- Enter a number in splines: splines. The form accepts 3 splines to 100 splines. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 6 splines as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Sets the cutter angle and the space available between splines.
- Get it right
- Count them on the drawing or the mating hub.
What this means: Width of each spline
- What it is
- Width of each spline across its two parallel sides.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 500 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 6 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Wider splines leave a narrower space for the cutter.
- Get it right
- Use the width the spline must have after milling, within its tolerance.
What this means: Root (minor) diameter of the splined shaft
- What it is
- Root diameter of the splined shaft, at the bottom of each space.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 2000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 23 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Sets the angle A and the chordal width at the root.
- Get it right
- Take the minor diameter from the spline drawing.
Method and formulas
- B = 360° ÷ N.
- sin A = W ÷ d, where A is the angle between the centre line of a spline and a radial line through the intersection of the root circle and one side of the spline.
- C = d sin(180° ÷ N − A), the chordal width at the root circle between adjacent splines.
- Example: 6 splines 6 mm wide on a 23 mm root diameter need a cutter angle of 60° and a chordal width of 5.9056 mm at the root.
Limitations
- For straight-sided splines milled one space at a time; hobbing is the more efficient method in production.
- Involute splines are made by other tools (the involute spline tools).
- The cutter width is the chord at the root circle; allow for the fit and tolerance of the spline width.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Order or grind a formed cutter for milling a splined shaft
- Check the space between splines at the root diameter
- Set up a dividing head job for a straight-sided spline
Who it is for
- Toolroom machinists
- Repair shops
- Tool designers
What you get
- Cutter angle B = 360° ÷ N
- Angle A at the root circle
- Chordal width C across the cutter’s concave edge
- Space between splines as a share of the pitch at the root
Interpreting the result
- The chordal width falls quickly as splines are made wider or more numerous; when it approaches zero the spaces can no longer be milled with one cutter pass.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 836. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These KEVOS® Library readings explain the method this tool uses, with worked examples.
Useful alongside · Library collection
Specialised machining operations: broaching, keyways, splines, knurling and indexing
What it covers: How keyways, splines, hexagon holes, knurls and evenly spaced features are made, when broaching pays, the CNC alternatives and the design details that keep these features economical.
KEVOS® tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.
Open the Spline Shaft Milling Cutter (Cutter Angle and Chordal Width at the Root) calculator