BIZOMAT MAKEOS · Threads
Thread Pitch Diameter by Three Wires (Accept or Reject)
Given my reading over three wires, what is the thread’s pitch diameter, and is it within the drawing limits?
Three-wire inspection of a symmetrical external thread: best wire size and the wire constant for the flank angle (as the three-wire tool), the measurement over wires expected at the largest and smallest permitted pitch diameter, the pitch diameter worked back from your reading, and accept or reject against the limits (which you can take from the metric thread limits tool for the class).
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Thread angle | choice | Included flank angle of the thread. |
| Pitch | mm | Pitch of the thread. |
| Largest pitch diameter allowed | mm | Upper limit of pitch diameter (for example from the metric thread limits tool). |
| Smallest pitch diameter allowed | mm | Lower limit of pitch diameter. |
| Wire diameter used (0 = best size) | mm | Diameter of the wires actually used; 0 uses the best size. |
| Reading over the wires | mm | Micrometer reading over the three wires. |
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 angle
- What it is
- The included angle between the two flanks of the thread form, which identifies the thread family. It sets the best wire size and the wire constant.
- Units and format
- Choose one of 4 options from the list: 60° (metric, unified); 55° (Whitworth); 29° (Acme); 30° (trapezoidal).
- Example
- The form opens with “60° (metric, unified)” selected as a worked example. Choose the option that matches your case.
- Get it right
- Choose by thread form: ISO metric and unified are 60°, Whitworth is 55°.
What this means: Pitch
- What it is
- The axial distance from one thread crest to the next, as given in the thread designation.
- 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
- Best wire size grows in proportion to pitch.
- Get it right
- For inch threads convert TPI to millimetres: pitch = 25.4 ÷ TPI.
What this means: Largest pitch diameter allowed
- What it is
- The upper limit of pitch diameter for the thread and its tolerance class, from the thread standard or the drawing. A reading that works back above it is rejected as oversize.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 2000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 8.994 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use pitch diameter limits, not major diameter limits.
What this means: Smallest pitch diameter allowed
- What it is
- The lower limit of pitch diameter for the thread and its tolerance class, from the thread standard or the drawing. A reading that works back below it is rejected as undersize.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 2000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 8.862 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- It must not exceed the largest pitch diameter, or the tool stops.
What this means: Wire diameter used (0 = best size)
- What it is
- The measured diameter of the three wires placed in the thread grooves under the micrometer. It changes the wire constant subtracted from the reading.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 20 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter 0 to use the best wire size; if you used other wires, enter their real diameter or the result will be wrong.
What this means: Reading over the wires
- What it is
- The micrometer reading taken over the three wires, two in grooves on one side and one on the other. The pitch diameter is worked back from it.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 2000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10.25 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The calculated pitch diameter moves one for one with the reading.
- Get it right
- Use light, consistent measuring force and the same wires stated above.
Method and formulas
- Best wire W = (P ÷ 2) ÷ cos(α ÷ 2); wire constant k = W [1 + 1 ÷ sin(α ÷ 2)] − (P ÷ 2) ÷ tan(α ÷ 2) (as the three-wire tool).
- Over-wire limits M = E + k at the largest and smallest pitch diameter E.
- Measured pitch diameter E = M_read − k; accept when it lies within the limits.
- Example: the reading should lie between 10.161 and 10.293 mm; 10.25 mm gives a pitch diameter of 8.951 mm.
Limitations
- No lead-angle correction; multi-start and coarse threads need it.
- Measuring force and wire accuracy affect the result at the micrometre level.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Inspect a thread with wires and a micrometer
- Set over-wire limits for a thread drawing
- Check a thread between gauges
Who it is for
- Inspectors
- Machinists
- Quality engineers
What you get
- Best wire and the wire constant
- Over-wire limits for the pitch diameter limits
- Pitch diameter from the reading and the decision
Interpreting the result
- Use wires close to the best size so they touch the flanks at the pitch line.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 1990–2003, 1867–1912. Topic reference; no source tables or recommended settings are reproduced.
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Open the Thread Pitch Diameter by Three Wires (Accept or Reject) calculator