MEASURING SCREW THREADS Machinery's Handbook, 31st Edition
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. M E P W 0866025 3 = − + The accompanying table contains these simplified formulas for different standard threads. Two formulas are given for each. The upper one is used when the measurement over wires, M , is known and the corresponding pitch diameter, E , is required; the lower formula gives the measurement M for a specified value of pitch diameter. These formulas are sufficiently accurate for checking practically all standard 60-degree single-thread screws because of the low lead angles, which vary from 1 ° 11 ′ to 4 ° 31 ′ in the American Standard Coarse-Thread Series. Bureau of Standards (now NIST) General Formula.— Formula (2) , which follows, com - pensates quite largely for the effect of the lead angle. It is from the National Bureau of Standards Handbook H 28 (1944), now FED-STD-H28. The formula, however, as here given has been arranged for finding the value of M (instead of E ). (2) This expression is also found in ANSI/ASME B1.2-1983 (R2017). The Bureau of Stan dards uses Formula (2) in preference to Formula (1) when the value of 0.5 W tan 2 B cos A cot A exceeds 0.00015, with the larger lead angles. If this test is applied to American Standard 60-degree threads, it will show that Formula (1) is generally applicable; but for 29-degree Acme or worm threads, Formula (2) (or some other that includes the effect of lead angle) should be employed. Notation Used in Formulas for Checking Pitch Diameters by Three-Wire Method A = one-half included thread angle in the axial plane A n = one-half included thread angle in the normal plane or in plane perpendicular to sides of thread = one-half included angle of cutter when thread is milled (tan A n = tan A × cos B ). (Note: Included angle of milling cutter or grinding wheel may equal the nominal included angle of thread, or may be reduced to whatever normal angle is required to make the thread angle standard in the axial plane. In either case, A n = one-half cutter angle.) B = lead angle at pitch diameter = helix angle of thread as measured from a plane perpendicular to the axis, tan B = L ÷ 3.1416 E D = basic major or outside diameter E = pitch diameter (basic, maximum, or minimum) for which M is required, or pitch diameter corresponding to measurement M F = angle required in Formulas (4b), (4d), and (4e) G = angle required in Formula (4) H = helix angle at pitch diameter and measured from axis = 90 ° − B or tan H = cot B H b = helix angle at R b measured from axis L = lead of thread = pitch P × number of threads S M = dimension over wires P = pitch = 1 ÷ number of threads per inch R b = radius required in Formulas (4) and (4e) S = number of “starts” or threads on a multiple-threaded worm or screw T = 0.5 P = width of thread in axial plane at diameter E T a = arc thickness on pitch cylinder in plane perpendicular to axis W = wire or pin diameter M = E − T cot A + W (1 + csc A + 0.5 tan 2 B cos A cot A )
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