Metric Trapezoidal Thread – Machining Calculations

Metric Trapezoidal Thread has a tooth profile of 30°, it is metric, so it uses the standard of the pitch, therefore this value along with the tooth profile angle are the only data we will need to calculate all the elements that make up this type of thread.

Known Data:
P: bolt pitch in millimeters.
α: 30°
D: Outside diameter of the bolt.

Unknown Data:
d: Height of the bolt thread.
e: Height of the nut thread.
f: Width of the root of the bolt thread and nut.
T: Generatrix of the thread taper.
c: Average height of the bolt thread.
a: Clearance of the screw crest with the nut.
b: Clearance of the screw root with the nut.
dT: Inside diameter of the nut.

Machining Formulas for the Metric Trapezoidal Thread

1. d = 0.5 (P) + a
   The values that a takes are:
   0.25 mm in pitch of 3 to 12 mm.
   0.5 mm in pitch of 14 to 26 mm.
2. e = 0.5 (P) + (2a – b)
   The values that b can take are:
   0.5 mm in pitch of 3 to 4 mm.
   0.75 mm in pitch of 5 to 12 mm.
   1.5 mm in pitch of 14 to 26 mm.
3. f = 0.634 (P) – (0.536 (d))
4. T = 0.933 (P)
5. c = 0.25 (P)

Example of Machining Calculation

Calculate all the necessary elements to create a metric trapezoidal profile screw if the screw pitch is 7 mm.

1. d = 0.5 (P) + a
   d = 0.5 (7) + 0.25, since the pitch is between 3 and 12 mm.
   d = 3.5 + 0.25
   d = 3.75 mm.
2. e = 0.5 (P) + (2a – b)
   e = 0.5 (7) + (2(0.25)-0.75)
   0.75 is the value that b takes, since the screw pitch is between 5 and 12 mm.
   e = 3.5 + (0.5 – 0.75)
   e = 3.5 + (-0.25)
   e = 3.25 mm.
3. f = 0.634 (P) – (0.536 (d))
   f = 0.634 (7) – (0.536 (3.75))
   f = 4.438 – (2.01)
   f = 2.428 mm.
4. T = 0.933 (P)
   T = 0.933 (7)
   T = 6.531 mm.
5. c = 0.25 (P)
   c = 0.25 (7)
   c = 1.75 mm.

You might also be interested in: How to Make the Square Thread on the Lathe.

An important fact about this type of threads is that they are standardized, meaning that according to a certain thread diameter there is a certain millimetric pitch. Here’s a table chart.

With this information, I hope to have explained the best way the features, concepts, and information about the Metric Trapezoidal Thread.

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