BIZOMAT MAKEOS · Threads
Helical Milling Lead and Change Gears
What lead does this helix have, and which change gears cut it on the dividing head?
Lead of a helix from the work diameter and helix angle, the table swivel angle, and the closest compound change-gear train between the table feed screw and the dividing head.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Work diameter (pitch diameter for gears) | mm | Diameter at which the helix angle is specified (pitch diameter for helical gears). |
| Helix angle (from the axis) | ° | Helix angle measured from the work axis. |
| Lead of the machine | mm | Table travel for one dividing-head spindle turn with equal gears (254 mm = 10 in on many machines). |
| Change gears available | choice | Change gears available. |
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: Work diameter (pitch diameter for gears)
- What it is
- The diameter of the work at which the helix angle is specified; for a helical gear, its pitch diameter.
- 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 60 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The required lead rises in proportion to diameter.
- Get it right
- Use the pitch diameter for gears, not the outside diameter.
What this means: Helix angle (from the axis)
- What it is
- The angle between the helix and the axis of the work; the table is also swivelled by this angle for the cutter to follow the helix.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 0.1° to 89°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 30° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger helix angle gives a shorter lead.
- Get it right
- Measure from the axis, not from a plane across the work; the two differ by 90°.
What this means: Lead of the machine
- What it is
- The table travel that turns the dividing-head spindle once when equal gears are fitted, which is a fixed property of the machine.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 254 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The required gear ratio is the needed lead divided by this value.
- Get it right
- Take it from the machine’s handbook or plate; it differs between machines.
What this means: Change gears available
- What it is
- Which set of change gears you have between the table feed screw and the dividing head; the tool searches only these gears.
- Units and format
- Choose one of 2 options from the list: Standard set: 24, 24, 28, 32, 40, 44, 48, 56, 64, 72, 86, 100; 24 to 100 in steps of 4.
- Example
- The form opens with “Standard set: 24, 24, 28, 32, 40, 44, 48, 56, 64, 72, 86, 100” selected as a worked example. Choose the option that matches your case.
- Get it right
- Choose the set you actually have, or the proposed train may use gears you do not own.
Method and formulas
- Lead = π D ÷ tan β.
- Gear ratio (driven product ÷ driver product) = required lead ÷ machine lead.
- Search all four-gear combinations of the set for the closest ratio.
- Example: 60 mm at 30° needs a 326.48 mm lead; drivers 24 and 56, driven 24 and 72 (error 0.026814%).
Limitations
- Gear fit on the quadrant is not checked.
- The swivel is set to the helix angle at the cutting diameter.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Mill helical gears, flutes and cams
- Find change gears for a required lead
- Check the lead error of a gear train
Who it is for
- Machinists
- Toolmakers
What you get
- Required lead
- Table swivel angle
- Best compound gear train and lead error
Interpreting the result
- Multiply the percentage error by the face width to see the lead error over the part.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2060–2062, 2205. Topic reference; no source tables or recommended settings are reproduced.
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