Measuring Pins and the Three-Wire Method for Pitch Diameter

A plain micrometer measures the major diameter of a thread, which tells you little about fit. What decides whether a screw and nut engage is the pitch diameter, an imaginary cylinder that sits on the flanks. You cannot put an anvil on it. The three-wire method gets at it indirectly: lay three precision measuring pins in the thread grooves and measure over them.

How the set-up works

Two wires go in adjacent grooves on one side of the thread and one wire in the groove opposite. The micrometer anvils close over the wires and the reading, M, is taken across all three. Because the wires touch the flanks at a known point, M is tied directly to the pitch diameter.

Choosing the wire: the best size

For a 60 degree metric thread on the ISO 68-1 basic profile, the best-size wire is w = 0.57735 x P. At that size the wire touches the flanks at the pitch line, so small errors in the flank angle barely affect the result. Use the nearest standard wire and recalculate, rather than a convenient wire that is far from best size.

The formula, with M12 worked through

For a 60 degree thread: pitch diameter d2 = M - 3w + 0.866025 x P, which rearranges to M = d2 + 3w - 0.866025 x P.

• M12 x 1.75: basic d2 = 12 - 0.6495 x 1.75 = 10.863 mm
• Best-size wire w = 0.57735 x 1.75 = 1.010 mm
• Expected M = 10.863 + 3.031 - 1.516 = 12.379 mm

If the micrometer reads 12.379 mm over the wires, the pitch diameter is on its basic size. Compare the actual pitch diameter with the limits for the class on the drawing (tolerance classes follow ISO 965-1), for example 6g for an external thread; our callout guide explains the class.

Where the error comes from

• Wire size. For a 60 degree thread, M changes by three times any change in wire diameter. A wire that is 1 micrometre off moves the result by 3 micrometres, so the wires need a calibrated diameter, and the calibration certificate belongs in the file.
• Measuring force. Too much force squeezes the wires into the flanks. Use the ratchet.
• Temperature. Measure at 20 °C or let parts and wires soak, as in our note on shop-floor temperature error.
• Thread form errors. The method assumes the profile is correct. It reports a pitch diameter that includes flank angle and pitch error, which is why it is paired with gauges, not used in place of them.

When to use wires and when a gauge

Wires give you a number, useful for setting up a thread-rolling or cutting process and for investigating a rejected part. A thread ring or plug gauge gives a faster pass or fail at the machine. We make both the gauges and the cylindrical measuring pins for this work. Send the thread size and pitch and we will quote the matching wire set.