Machinery's Handbook, 31st Edition
2126 MEASURING SCREW THREADS These formulas are based upon a thread groove of zero lead angle because ordinary variations in the lead angle have little effect on the wire diameter and it is desirable to use one wire size for a given pitch regardless of the lead angle. A theoretically correct solution for finding the exact size for pitch-line contact involves the use of cumbersome indeterminate equations with solution by successive trials. The accompanying table gives the wire sizes for both American Standard (formerly, US Standard) and the Whitworth Standard Threads. The following formulas for determining wire diameters do not give the extreme theoretical limits, but the smallest and largest practicable sizes. The diameters in the table are based upon these approximate formulas.
Smallest wire diameter = 0.56 × pitch Largest wire diameter = 0.90 × pitch Diameter for pitch-line contact = 0.57735 × pitch Smallest wire diameter = 0.54 × pitch Largest wire diameter = 0.76 × pitch Diameter for pitch-line contact = 0.56369 × pitch
American Standard
Whitworth
Measuring Wire Accuracy.— A set of three measuring wires should have the same diam eter within 0.0002 (5.08 m m) inch. To measure the pitch diameter of a screw-thread gage to an accuracy of 0.0001 inch (2.54 m m) by means of wires, it is necessary to know the wire diameters to 0.00002 (0.51 m m) inch. If the diameters of the wires are known only to an accuracy of 0.0001 (2.54 m m) inch, an accuracy better than 0.0003 (7.62 m m) inch in the measurement of pitch diameter cannot be expected. The wires should be accurately fin ished hardened steel cylinders of the maximum possible hardness without being brittle. The hardness should not be less than that corresponding to a Knoop indentation number of 630. A wire of this hardness can be cut with a file only with difficulty. The surface should not be rougher than the equivalent of a deviation of 3 microinches (0.0762 m m) from a true cylindrical surface. Measuring or Contact Pressure.— In measuring screw threads or screw-thread gages by the 3-wire method, variations in contact pressure will result in different readings. The ef - fect of a variation in contact pressure in measuring threads of fine pitches is indicated by the difference in readings obtained with pressures of 2 and 5 pounds (0.91 and 2.27 kg) in checking a thread plug gage having 24 threads per inch. The reading over the wires with 5 pounds (2.27 kg) pressure was 0.00013 inch (3.302 m m) less than with 2 pounds (0.91 kg) pressure. For pitches finer than 20 threads per inch (0.05 inch or 1.27 mm pitch), a pres - sure of 16 ounces (0.45 kg) is recommended by the National Bureau of Standards, now National Institute of Standards and Technology (NIST). For pitches of 20 threads per inch and coarser, a pressure of 2 1 ∕ 2 pounds (1.13 kg) is recommended. For Acme threads, the wire presses against the sides of the thread with a pressure of approximately twice that of the measuring instrument. To limit the tendency of the wires to wedge in between the sides of an Acme thread, it is recommended that pitch-diameter measurements be made at 1 pound on 8 threads per inch and finer, and at 2 1 ∕ 2 pounds for pitches coarser than 8 threads per inch (0.125 inch or 3.175 mm pitch). Approximate Three-Wire Formulas That Do Not Compensate for Lead Angle.— A general formula in which the effect of lead angle is ignored is as follows (see accompanying nota - tion used in formulas): (1) This formula can be simplified for any given thread angle and pitch. To illustrate, because T = 0.5 P , M = E − 0.5 P cot 30 ° + W (1 + 2), for a 60-degree thread, such as the American Standard, cot csc M E T A W A 1 = − + + ^ h
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