Machinery's Handbook, 31st Edition
2128
MEASURING SCREW THREADS Formulas for Checking Pitch Diameters of Screw Threads
The formulas below do not compensate for the effect of the lead angle upon measurement M , but they are sufficiently accurate for checking standard single-thread screws unless exceptional accuracy is required. See accompanying information on effect of lead angle; also matter relating to measuring wire sizes, accuracy required for such wires, and contact or measuring pressure. The approximate best wire size for pitch-line contact may be obtained by the formula . sec W 05 pitch included thread angle # # = For 60-degree threads, W = 0.57735 × pitch. 2 1
D E
M
W
Formulas for determining measurement M corresponding to correct pitch diameter and the pitch diameter E corresponding to a given measurement over wires. a
Form of Thread
American National Standard Unified British Standard Whitworth British Association Standard Lowenherz Thread
When measurement M is known, When pitch diameter E is used in formula, . E M The American Standard formerly was known as US Standard. P W 086603 3 = + − . M E
P W 086603 3 = − +
. . E M P W 0 9605 3 1657 = + −
When measurement M is known, When pitch diameter E is used in formula, When measurement M is known, When pitch diameter E is used in formula, When measurement M is known, When pitch diameter E is used in formula, When measurement M is known, When pitch diameter E is used in formula,
. P W 0 9605 3 1657 = − + .
M E
. . E M P W 1 1363 3 4829 = + −
. P W 1 1363 3 4829 = − + .
M E
. E M P
W 32359 = + −
. M E P
W 32359 = − +
. E M
P W 086603 3 = + −
Sharp V-Thread
. M E
P W 086603 3 = − +
International Standard
Use the formula above for the American National Standard Unified Thread. See accompanying paragraph on Buckingham Exact Involute Helicoid Formula Applied to Screw Threads . See Buckingham Formulas page 2132; also Three-Wire Measurement of Acme and Stub Acme Thread Pitch Diameter . Different forms of buttress threads are used. See paragraph on Three-Wire Method Applied to Buttress Threads .
Pipe Thread
Acme and Worm Threads Buttress Form of Thread
a The wires must be lapped to a uniform diameter and it is very important to insert in the rule or formula the wire diameter as determined by precise means of measurement. Any error will be multiplied. See paragraph on Wire Sizes for Checking Pitch Diameters of Screw Threads on page 2125. Why Small Thread Angle Affects Accuracy of Three-Wire Measurement.— In measuring or checking Acme threads, or any others having a comparatively small thread angle A , it is particularly important to use a formula that compensates largely, if not entirely, for the ef - fect of the lead angle, especially in all gage and precision work. The effect of the lead angle on the position of the wires and upon the resulting measurement M is much greater in a 29-degree thread than in a higher thread angle such, for example, as a 60-degree thread. This effect results from an increase in the cotangent of the thread angle as this angle be - comes smaller. The reduction in the width of the thread groove in the normal plane due to
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