BIZOMAT MAKEOS · Threads
Change Gears for Thread Cutting
Which change gears cut this thread lead on this lathe?
Best simple and compound change-gear trains from a standard gear set to cut a required metric or inch lead with a given leadscrew, with the resulting lead error.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Thread to cut is given as | choice | Whether the thread is metric (pitch) or inch (TPI). |
| Thread to cut | mm or TPI | Pitch in millimetres or threads per inch of the thread to cut. |
| Leadscrew is given as | choice | Leadscrew specification. |
| Leadscrew | mm or TPI | Leadscrew pitch or threads per inch, from the lathe plate or manual. |
| Fixed ratio in the headstock (spindle to stud) | :1 | Any fixed reduction between the spindle and the first change-gear stud (1 if none). |
| Gear set | choice | The change gears available; check your actual set (one of each size assumed). |
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: Thread to cut is given as
- What it is
- How the thread to cut is specified: as a pitch in millimetres (metric) or as threads per inch (inch).
- Units and format
- Choose one of 2 options from the list: Pitch in mm; Threads per inch.
- Example
- The form opens with “Pitch in mm” selected as a worked example. Choose the option that matches your case.
- Get it right
- Match it to the number entered for the thread to cut.
What this means: Thread to cut
- What it is
- The thread to be cut on the lathe: its pitch in millimetres, or its threads per inch, according to the unit chosen above.
- Units and format
- Enter a number in mm or TPI: mm or TPI. The form accepts 0.000001 mm or TPI to 1000 mm or TPI. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.5 mm or TPI as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- For a multi-start thread the gearing must produce the lead, not the pitch.
What this means: Leadscrew is given as
- What it is
- How the lathe leadscrew is specified: threads per inch or pitch in millimetres, as stamped on the lathe or given in its manual.
- Units and format
- Choose one of 2 options from the list: Threads per inch; Pitch in mm.
- Example
- The form opens with “Threads per inch” selected as a worked example. Choose the option that matches your case.
- Get it right
- Imperial lathes usually have TPI leadscrews; check the plate rather than assuming.
What this means: Leadscrew
- What it is
- The leadscrew’s threads per inch or pitch in millimetres, according to the unit chosen, from the lathe plate or manual.
- Units and format
- Enter a number in mm or TPI: mm or TPI. The form accepts 0.000001 mm or TPI to 1000 mm or TPI. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 8 mm or TPI as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Measure it if the plate is missing; the result is only as exact as this value.
What this means: Fixed ratio in the headstock (spindle to stud)
- What it is
- Any fixed gearing inside the headstock before the change gears, given as the number of stud turns per spindle turn (the factor the tool divides the required ratio by).
- Units and format
- Enter a number in :1: a ratio to one (type 3 for 3:1). The form accepts 0.01 :1 to 100 :1. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 :1 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- The tool treats this as stud speed ÷ spindle speed: a stud running slower than the spindle needs a value below 1. Use 1 if there is no fixed gearing.
What this means: Gear set
- What it is
- The range of change gears you have, one of each size, including the 127-tooth gear used for exact metric–inch conversion.
- Units and format
- Choose one of 2 options from the list: 20 to 120 in steps of 5, plus 127; 24 to 96 in steps of 4, plus 127.
- Example
- The form opens with “20 to 120 in steps of 5, plus 127” selected as a worked example. Choose the option that matches your case.
- Get it right
- Check that every gear in the chosen set is actually in your cabinet before cutting.
Method and formulas
- Required ratio (driver ÷ driven product) = lead to cut ÷ (leadscrew lead × fixed ratio), all leads in mm.
- Simple train A ÷ B; compound train (A ÷ B) × (C ÷ D), each gear used once.
- Error = (train ratio ÷ required − 1) × 100%; 25.4 mm = 127 ÷ 5 × 1 mm makes 127-tooth gears exact for metric–inch conversions.
- Example: 1.5 mm pitch on an 8 TPI leadscrew: drivers 20 and 75, driven 25 and 127 (error 0%).
Limitations
- Gear meshing and clearance on the banjo are not checked; some compound trains may not fit your lathe.
- One of each gear size is assumed.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Set up a manual lathe for a non-standard pitch
- Cut metric threads with an inch leadscrew (or the reverse)
- Check the error of an approximate gear train
Who it is for
- Machinists
- Toolmakers
What you get
- Required gear ratio
- Best two-gear train and its error
- Best four-gear compound train and its error
Interpreting the result
- For an approximate train, multiply the error by the thread length to see the accumulated lead error.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2043–2049. Topic reference; no source tables or recommended settings are reproduced.
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