Machinery's Handbook, 31st Edition
2138 MEASURING SCREW THREADS Measuring Taper Screw Threads by Three-Wire Method.— When the 3-wire method is used in measuring a taper screw thread, the measurement is along a line that is not per pendicular to the axis of the screw thread, the inclination from the perpendicular equaling one-half the included angle of the taper. The formula that follows compensates for this inclination resulting from contact of the measuring instrument surfaces, with two wires on one side and one on the other. The taper thread is measured over the wires in the usual manner except that the single wire must be located in the thread at a point where the effec - tive diameter is to be checked (as described more fully later). The formula shows the di - mension equivalent to the correct pitch diameter at this given point. The general formula for taper screw threads follows: sec csc cot M b E a N W a 2 1 = − + + ^ ^ h h ⁄ where M = measurement over the 3 wires E = pitch diameter a = one-half the angle of the thread N = number of threads per inch W = diameter of wires; and b = one-half the angle of taper. This formula is not theoretically correct but it is accurate for screw threads having tapers of 3 ∕ 4 inch per foot or less. This general formula can be simplified for a given thread angle and taper. The simplified formula following (in which P = pitch) is for an American National Standard pipe thread: . . M E P W 100049 0866025 3 # # = − + ^ h Standard pitch diameters for pipe threads will be found in the section “American Pipe Threads,” which also shows the location, or distance, of this pitch diameter from the end of the pipe. In using the formula for finding dimension M over the wires, the single wire is placed in whatever part of the thread groove locates it at the point where the pitch diameter is to be checked. The wire must be accurately located at this point. The other wires are then placed on each side of the thread that is diametrically opposite the single wire. If the pipe thread is straight or without taper, . M E P W 0866025 3 # # = − + ^ h Application of Formula to Taper Pipe Threads: To illustrate the use of the formula for taper threads, assume that dimension M is required for an American Standard 3-inch pipe thread gage. Table 1a starting on page 2090 shows that the 3-inch size has 8 threads per inch, or a pitch of 0.125 inch, and a pitch diameter at the gaging notch of 3.3885 inches. Assume that the wire diameter is 0.07217 inch: Then when the pitch diameter is correct . . . . . . M 100049 3 3885 0 866025 0 125 3 0 07217 3 495 inches # # = − + = ^ h Pitch Diameter Equivalent to a Given Measurement Over the Wires: The formula fol lowing may be used to check the pitch diameter at any point along a tapering thread when measurement M over wires of a given diameter is known. In this formula, E = the effective or pitch diameter at the position occupied by the single wire. The formula is not theoreti cally correct but gives very accurate results when applied to tapers of 3 ∕ 4 inch per foot or less. . . E M P W 100049 0866025 3 # # # = + − ^ h Example: Measurement M = 3.495 inches at the gaging notch of a 3-inch pipe thread and the wire diameter = 0.07217 inch. Then
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