BIZOMAT MAKEOS · Threads
Change-Gear Threading Set-up (Gear Train, Pitch Error, Thread Depth, Passes)
To cut this metric thread on a lathe with an inch leadscrew (or the other way round), which change gears do I fit, how accurate is the pitch, and how deep and in how many passes do I cut?
Set-up for single-point screw cutting on a lathe with change gears: the ratio needed from the thread lead, leadscrew and fixed headstock ratio, the best simple and compound gear trains from the gear set with their pitch errors (as the change gears tool), and the thread height, pitch diameter and number of passes for a constant-area infeed from your first-pass depth (as the metric thread tool for thread depth), checked against the pitch error you accept.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Thread nominal diameter | mm | Nominal diameter of the metric thread. |
| Thread pitch to cut | mm | Pitch of the thread to cut. |
| Leadscrew is given as | choice | Whether the leadscrew is inch (threads per inch) or metric (pitch). |
| Leadscrew | TPI or mm | Leadscrew threads per inch or pitch. |
| Fixed ratio in the headstock (spindle to stud) | :1 | Ratio between spindle and stud gear fixed inside the headstock. |
| Gear set | choice | Change gears you have. |
| Largest pitch error | % | Largest pitch error you accept from the gear train. |
| First pass depth (radial) | mm | Depth of the first pass; later passes get shallower to keep the chip area constant. |
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 nominal diameter
- What it is
- The nominal diameter of the metric thread to be cut, used for its pitch and minor diameters.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 12 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Thread pitch to cut
- What it is
- The pitch of the metric thread to be cut: the axial distance between neighbouring crests, which the gear train must reproduce.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 50 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.5 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Thread height rises with the pitch, and the number of passes with its square.
What this means: Leadscrew is given as
- What it is
- Whether the lathe’s leadscrew is specified in threads per inch (an inch leadscrew) or as a pitch in millimetres (a metric leadscrew).
- 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.
What this means: Leadscrew
- What it is
- The leadscrew value in the unit chosen above: threads per inch for an inch leadscrew, or pitch in millimetres for a metric one.
- Units and format
- Enter a number in TPI or mm: TPI or mm. The form accepts 0.000001 TPI or mm to 1000 TPI or mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 8 TPI or mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- The meaning follows the unit choice; a TPI value typed with ‘Pitch in mm’ selected gives a wrong ratio.
What this means: Fixed ratio in the headstock (spindle to stud)
- What it is
- The fixed gear ratio inside the headstock between the spindle and the stud gear that drives the change gears, from the lathe manual.
- 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
- Enter 1 if the stud gear turns at spindle speed.
What this means: Gear set
- What it is
- The change gears you have available; the tool searches them for the best simple and compound gear trains.
- 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.
What this means: Largest pitch error
- What it is
- The largest pitch error from the gear train that you accept, as a percentage of the thread pitch.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 0% to 10%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.05% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- A percentage error adds up along the thread, so long threads or long engagements need a smaller limit.
What this means: First pass depth (radial)
- What it is
- The radial infeed depth of the first threading pass; later passes are made shallower to keep the chip area constant.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.01 mm to 5 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.3 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 falls with the square of the first pass depth.
Method and formulas
- Ratio = thread lead ÷ (leadscrew lead × fixed ratio); best two- and four-gear trains from the set (as the change gears tool).
- External thread height h₃ = 0.6134P; pitch diameter d₂ = d − 0.6495P (as the metric thread tool).
- Constant-area infeed: depth after pass k = a₁ √k, so passes = ⌈(h₃ ÷ a₁)²⌉.
- Example: fit drivers 20 and 75, driven 25 and 127 (error 0%); cut 0.92015 mm deep in 10 passes.
Limitations
- Gear fit on the quadrant and the idler arrangement must be checked on the machine.
- Infeed passes are a starting plan; the last passes are often spring passes.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Cut a metric thread on an imperial lathe
- Check a gear train’s pitch error
- Plan passes for single-point threading
Who it is for
- Machinists
- Toolroom staff
- Apprentices
What you get
- Ratio needed and best gear trains with their errors
- Thread height and pitch diameter
- Passes for the constant-area infeed
Interpreting the result
- Metric threads on an inch leadscrew need a 127-tooth gear for an exact ratio; without it, check the error over the thread length.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2043–2049, 1867–1890. Topic reference; no source tables or recommended settings are reproduced.
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Open the Change-Gear Threading Set-up (Gear Train, Pitch Error, Thread Depth, Passes) calculator