BIZOMAT MAKEOS · Threads
Three-Wire Measurement with Lead Angle (Buckingham)
What should the measurement over wires read for this coarse-lead or multi-start thread or worm?
Measurement over three wires including the effect of lead angle by Buckingham’s simplified formula, with the wire size the formula requires, for worms, Acme and multi-start threads.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Included thread angle | ° | Included angle of the thread form (60° unified/metric, 29° Acme and worms, 40° worms). |
| Angle measured in | choice | Whether the stated angle is in the axial plane or the normal plane. |
| Axial pitch | mm or in | Axial pitch (distance between adjacent threads), in the same unit as the pitch diameter. |
| Number of starts | starts | Number of thread starts; lead = starts × pitch. |
| Pitch diameter | mm or in | Pitch diameter to be checked. |
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: Included thread angle
- What it is
- The full included angle between the two flanks of the thread or worm form, measured in the plane chosen below.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 10° to 90°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 29° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Give the full included angle, not the flank (half) angle.
What this means: Angle measured in
- What it is
- Whether the stated thread angle is measured in the axial plane (along the axis, as when the cutter matches the axial form) or in the normal plane (square to the thread helix).
- Units and format
- Choose one of 2 options from the list: Axial plane (cutter matches the axial thread form); Normal plane (cutter angle normal to the thread).
- Example
- The form opens with “Axial plane (cutter matches the axial thread form)” selected as a worked example. Choose the option that matches your case.
- Get it right
- Take this from the drawing or the way the thread is cut; the two give different wire sizes on coarse leads.
What this means: Axial pitch
- What it is
- The axial pitch: the distance between adjacent thread flanks or teeth along the axis, whatever the number of starts.
- Units and format
- Enter a number in mm or in: millimetres or inches, as long as every length uses the same unit. The form accepts 0.000001 mm or in to 1000 mm or in. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 6.35 mm or in as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The wire diameter is directly proportional to the pitch.
- Get it right
- Do not enter the lead on a multi-start thread; the tool multiplies pitch by starts itself. Use the same unit as the pitch diameter.
What this means: Number of starts
- What it is
- The number of separate thread helices wound side by side; count the thread ends visible at the end of the screw or worm.
- Units and format
- Enter a number in starts: a number of thread starts. The form accepts 1 starts to 20 starts. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2 starts as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More starts give a larger lead angle and a bigger correction over the simple formula.
- Get it right
- The lead is starts × pitch, so a two-start thread advances twice as far per turn.
What this means: Pitch diameter
- What it is
- The pitch diameter of the thread or worm to be checked, the diameter at which tooth and space widths are equal, normally the drawing’s nominal value.
- Units and format
- Enter a number in mm or in: millimetres or inches, as long as every length uses the same unit. The form accepts 0.000001 mm or in to 100000 mm or in. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 40 mm or in as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A smaller pitch diameter gives a larger lead angle for the same lead.
- Get it right
- Use the same unit as the pitch.
Method and formulas
- Lead angle B = atan(lead ÷ πE); half-angle A = included ÷ 2.
- Normal half-angle An: tan An = tan A cos B (axial form) or An = A (normal form). Axial thickness T = P/2.
- Wire diameter W = T cos B ÷ cos An; M = E + W(1 + sin An) (Buckingham’s formula 3).
- The simple formula without lead angle is shown for comparison.
- Example: a 2-start 29° thread, pitch 6.35, on 40 pitch diameter needs 3.2618 wires and reads 44.075.
Limitations
- Very accurate for lead angles below about 8–10°; for extreme accuracy at larger angles use the involute helicoid method.
- The wire diameter must equal the calculated value for the formula to apply directly.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Inspect worms and multi-start threads accurately
- Choose wire size for a coarse-lead thread
- See how much lead angle changes the reading
Who it is for
- Quality inspectors
- Toolmakers
- Metrology technicians
What you get
- Lead angle
- Normal half-angle
- Wire diameter required by the formula
- Measurement over wires and the simple-formula reading
Interpreting the result
- If your wires differ from W, use the closest available set and the simple formula with a correction, or measure with balls.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 1990–2003. Topic reference; no source tables or recommended settings are reproduced.
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Open the Three-Wire Measurement with Lead Angle (Buckingham) calculator