MEASURING SCREW THREADS Machinery's Handbook, 31st Edition
2139
. . E 1 00049 3 495 0 866025 0 125 3 0 07217 3 3885 inches # # # = + − = ^ h . . . . Pitch Diameter at Any Point Along Taper Screw Thread: When the pitch diameter in any position along a tapering thread is known, the pitch diameter at any other position may be determined as follows: Multiply the distance (measured along the axis) between the location of the known pitch diameter and the location of the required pitch diameter, by the taper per inch or by 0.0625 for American National Standard pipe threads. Add this product to the known diameter, if the required diameter is at a large part of the taper, or subtract if the required diameter is smaller. Example: The pitch diameter of a 3-inch American National Standard pipe thread is 3.3885 at the gaging notch. Determine the pitch diameter at the small end. The table start ing on page 2090 shows that the distance between the gaging notch and the small end of a 3-inch pipe is 0.77 inch. Hence the pitch diameter at the small end = 3.3885 − (0.77 × 0.0625) = 3.3404 inches. Three-Wire Method Applied to Buttress Threads.— The angles of buttress threads vary somewhat, especially on the front or load-resisting side. Formula (1) , which follows, may be applied to any angles required. In this formula, M = measurement over wires when pitch diameter E is correct; A = included angle of thread and thread groove; a = angle of front face or load-resisting side, measured from a line perpendicular to screw thread axis; P = pitch of thread; and W = wire diameter. (1) cos W A a csc M E P 1 # = − + + : − a k ; E D
A 2
2
tan tan a +
A a −
h
^
P
P
1 8 P
1 8 P
W
W
45°
50°
3 4 P
5°
M
M
45°
90°
50°
1 8 P
1 8 P
For given angles A and a , this general formula may be simplified as shown by Formulas (3) and (4) . These simplified formulas contain constants with values depending upon angles A and a . Wire Diameter: The wire diameter for obtaining pitch-line contact at the back of a but tress thread may be determined by the following general Formula (2): (2) 45-Degree Buttress Thread: The buttress thread shown by the diagram at the left, has a front or load-resisting side that is perpendicular to the axis of the screw. Measurement M equivalent to a correct pitch diameter E may be determined by Formula (3): (3) Wire diameter W for pitch-line contact at back of thread = 0.586 × pitch. . M E P W 34142 # = − + ^ h cos cos W P 1 = + ` A a j
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