BIZOMAT MAKEOS · Manufacturing
Polygon Milling Set-up (Stock Size, Depth of Cut, Indexing)
To mill a hexagon (or any regular polygon) on round bar, what stock diameter do I need for sharp corners, how deep is each flat, and what index setting moves between flats?
Set-up for milling a regular polygon on round stock with a dividing head: side length, across-flats and across-corners sizes (as the regular polygon tool), whether the stock is large enough for full corners, depth of cut to each flat and the passes for your largest depth of cut, and the simple indexing setting between flats (as the simple indexing tool).
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Number of sides | Number of flats on the polygon. | |
| Across flats | mm | Distance across opposite flats (or a flat and the opposite corner for odd numbers, measured as the inscribed circle diameter). |
| Round stock diameter | mm | Diameter of the round bar. |
| Largest depth of cut per pass | mm | Deepest cut you take in one pass. |
| Dividing head worm ratio | :1 | Worm ratio of the dividing head. |
| Index plates available | choice | Index plates you have. |
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 sides
- What it is
- The number of flats on the regular polygon, for example six for a hexagon, which sets the side length and the indexing between flats.
- Units and format
- Enter a plain number with no unit. The form accepts 3 to 100. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 6 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Crank turns between flats are the worm ratio divided by this number.
- Get it right
- For an odd number of sides, measure from a flat to the opposite corner rather than across flats.
What this means: Across flats
- What it is
- The size across opposite flats of the finished polygon; for an odd number of sides use the diameter of the circle that touches every flat (the inscribed circle).
- 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 24 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Side length and across-corners size rise in proportion; a larger size reduces the depth of cut.
- Get it right
- For an odd polygon do not enter the flat-to-corner measurement; enter the inscribed circle diameter.
What this means: Round stock diameter
- What it is
- The diameter of the round bar the polygon is milled from.
- 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 30 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The depth of cut to each flat is half of stock minus across flats, so a larger bar means more passes.
- Get it right
- For sharp corners the bar must be at least the across-corners size; a smaller bar leaves round corners.
What this means: Largest depth of cut per pass
- What it is
- The deepest cut you take in one pass on the milling machine for this material, cutter and set-up.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.01 mm to 100 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The number of passes is the depth to each flat divided by this, rounded up.
- Get it right
- Base it on your cutter maker’s data and the rigidity of the dividing-head set-up.
What this means: Dividing head worm ratio
- What it is
- The worm ratio of the dividing head: the number of crank turns that rotate the spindle once.
- Units and format
- Enter a number in :1: a ratio to one (type 3 for 3:1). The form accepts 1 :1 to 200 :1. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 40 :1 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Crank turns between flats are this ratio divided by the number of sides.
- Get it right
- Enter only the first number of the ratio, as in 40 for a 40:1 head.
What this means: Index plates available
- What it is
- The set of index plates you have for the dividing head, which decides which hole circles the tool can use for a fractional crank turn.
- Units and format
- Choose one of 2 options from the list: Brown & Sharpe plates 1–3; Cincinnati standard plate (both sides).
- Example
- The form opens with “Brown & Sharpe plates 1–3” selected as a worked example. Choose the option that matches your case.
- Get it right
- Choose the set actually in the workshop; if no circle suits, the tool reports that differential indexing is needed.
Method and formulas
- Side = across flats × tan(180° ÷ n); across corners = side ÷ sin(180° ÷ n) (as the regular polygon tool).
- Full corners need stock ≥ across corners; depth of cut to each flat = (stock − across flats) ÷ 2; passes = ⌈depth ÷ largest cut⌉.
- Crank turns between flats = ratio ÷ n (as the simple indexing tool).
- Example: a 24 mm hexagon needs 27.713 mm across corners; cut 3 mm deep in 2 passes; index 6 turns and 10 holes in the 15-hole circle.
Limitations
- Sharp corners; chamfered corners allow smaller stock.
- Simple indexing only.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Mill a hexagon or square on a bar end
- Choose stock size for a polygon
- Prepare the index setting for flats
Who it is for
- Machinists
- Toolroom staff
- Maintenance fitters
What you get
- Side, across-flats and across-corners sizes
- Stock check, depth of cut and passes
- Index setting
Interpreting the result
- Stock between the across-flats and across-corners sizes gives a polygon with rounded corners, which is often acceptable for nuts and keys.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 76, 81–82, 2107–2121. Topic reference; no source tables or recommended settings are reproduced.
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Open the Polygon Milling Set-up (Stock Size, Depth of Cut, Indexing) calculator