Pitch Diameter Formula

When cutting screw threads the mechanic  must have some way to check the threads. Threads should be measured at the pitch diameter. The pitch diameter is a point along the flank or angular surface of the thread

. The thread pitch micrometer is an excellent and easy way to measure threads, but one pitch micrometer will not measure all of the different thread types and sizes. The thread ring gage will tell you whether the thread is right or wrong, but it will not give you an accurate account of the thread depth. The three-wire method is considered to be one of the most accurate and versatile ways of measuring threads. The three-wire method uses three lapped and polished wires and a micrometer to measure the pitch diameter of the thread

The wires are placed in the threads and a micrometer is used to measure over the top of the wires. Different thread types and thread sizes require different size wires. The three-wire method of thread measurement can be used for all types of threads including Unified, Acme, and Buttress thread forms.

To help you understand the three-wire method of thread measurement, we will use an example thread of 1.250-5 ACME-2G . The first piece of information we need to acquire is the "best wire size." The best wire size is the size of the wire that will contact the thread at the pitch diameter. The best wire size can be calculated using a formula, Begin by looking in the index under Thread, Acme, wire method of testing. Turn to this section and find the table which gives the wire sizes for measuring Acme threads with lead angles less than 5 degrees. Now look for the column that shows 5 threads per inch. You should find that the table gives you 0.10329 as the best wire size.  The table also gives you minimum and maximum wire size limits. Make a note of the best wire size.

Now we need to find out what the measurement over the wires should be. Within the same unit you will find a paragraph entitled Three Wire Measurement of Acme and Stub Acme Thread Pitch Diameters. Within this paragraph it will tell you where to find the Approximate Three Wire Formula. The Approximate Three Wire Formula "SIMPLIFIED VERSION" should read as follows:

M = E - 0.86603P + 3W

Where:

     M = the measurement over the wires

     E = the pitch diameter

     P = the pitch or (1 divided by the number of threads per inch)

    W= the wire size

We really only need to find the pitch diameter to solve the formula. We have the wire size. We know the pitch is 1/5 or 0.2 . To find the pitch diameter, go back to the index in the Machinery’s Handbook. Look in the index for Screw threads and threads systems. Under Screw threads and threads systems find Acme. Turn to this section and find the table that gives the Limiting Dimension for American National Standards for General Purpose Acme Single-Start Screw threads. In this table find the Class 2G, Pitch Diameter, Maximum and Minimum limiting diameters for the 1.250-5 ACME-2G thread. You should find that the table gives you 1.1210 as the minimum size and 1.1410 as the maximum size for the pitch diameter calculation. We will use the median dimension of 1.1310 for our formula calculation. Now that we have all of the information, let's plug the numbers into the formula.

M = E - 0.86603P + 3W

M = 1.131-(0.86603 X 0.2) + (3 X 0.10329)

M = 1.131 - 0.173206 + 0.30987

M = 1.268 (micrometer measurement over the wires)