Calculation Formulas for Metric, Imperial, And American Threads

Calculation formulas for metric, imperial, and American threads

In the grand system of modern industrial precision operation, threaded connection, as a basic and key fastening method, is like the joint of the industrial "skeleton", ensuring the stability and coordinated operation of various mechanical devices. From precision electronic instruments to giant engineering equipment, threads are everywhere. However, due to the diversified paths of global industrial development, metric, imperial, and American threads are each a system, and their calculation formulas are even more complex and critical. In order to help the majority of industrial practitioners and mechanical enthusiasts clearly master these core knowledge, this article carefully organizes the calculation formulas of metric, imperial, and American threads to provide a comprehensive and detailed reference for your work and study.

Metric thread (MM thread)

Thread depth = 0.6495*pitch P

(tooth angle 60 degrees)

Internal thread diameter = nominal diameter-1.0825*P

M20x2.5-6H/7g (right hand)-(single thread)-(metric coarse thread)

(nominal diameter 20mm) (pitch 2.5mm)

(internal thread matching grade 6H)

(external thread matching grade 7g)

Left-double-M20x1.5 (left hand)-(double thread)-(metric fine thread)

(nominal diameter 20mm) (pitch 1.5mm)

American thread

(unified standard thread)

Thread depth = 0.6495*(25.4/number of teeth per inch)

(tooth angle 60 degrees)

3/4-10UNC-2A

(UNC coarse thread)(UNF fine thread)

(1A 2A 3A external thread tolerance level)

(1B 2B 3B internal thread tolerance level)

UNC American unified standard coarse thread

Outer diameter 3/4 inch, 10 teeth per inch

External thread 2nd grade tolerance

Pipe thread (British PT)

Thread depth = 0.6403*(25.4/number of teeth per inch)

(tooth angle 55 degrees)

PT 3/4-14 (tapered pipe thread) tapered pipe thread, taper ratio 1/16

For 3/4 inch pipe, 14 teeth per inch

Thread

(PS straight thread)(PF fine thread)

Thread depth = 0.6403*(25.4/number of threads per inch)

(tooth angle 55 degrees)

PS 3/4-14 (straight pipe thread)

PF1 1/8-16 (straight pipe thread)

(fine thread)

Straight pipe thread

For 3/4 inch pipe, 14 threads per inch

For 1 1/8 inch pipe, 16 threads per inch

Pipe thread (American NPT)

(tooth angle 60 degrees)

NPT 3/4-14 (tapered pipe thread) Tapered pipe thread, taper ratio 1/16

For 3/4 inch pipe, 14 threads per inch

Trapezoidal thread

(30 degrees Metric)

TM40*6 Nominal diameter 40mm Pitch 6.0mm

Trapezoidal thread

(29 degrees Acme thread)

TW26*5 OD 26mm, 5 threads per inch

Square thread

Calculation of threading

Considerations Calculation formula

Conversion between metric and imperial threads Number of threads per inch n = 25.4 / pitch P

Pitch P = 25.4 / number of threads per inch n

Speed determined by workpiece material and tool Speed N = (1000 circumference V) / (pi p * diameter D)

Speed determined by machine structure

The influence of rapid movement of tool holder Maximum threading speed N = 4000/P

The influence of rapid movement acceleration and deceleration of tool holder

Calculation of cutting point and retraction point

(Calculation of incomplete thread) Minimum cutting distance L1

L1 = (pitch P) * (spindle speed S) / 500

Minimum retraction distance L2

L2 = (pitch P) * (spindle speed S) / 2000

Depth of thread and root diameter d Depth of thread h =0.6495 * P

Diameter of the tooth base d = nominal outer diameter D - 2 * h

Example:

Turn external thread 3/4"-10UNC 20mm long

Conversion between metric and imperial threads Pitch P = 25.4 / (number of threads per inch n)

P = 25.4 / 10 = 2.54mm

Speed determined by workpiece material and tool Outer diameter D = 3 / 4 inches = 25.4 * (3/4) = 19.05MM

Speed N = (1000 circumference V) / (circle p * diameter D)

N = 1000V / pD = 1000 * 120 / (3.1416*19.05)

=2005 rpm (revolutions/minute)

Speed determined by machine structure Influence of rapid movement of tool holder Maximum speed N for thread turning =4000 / P

N = 4000/2.54 = 1575 rpm

The speed determined by the workpiece material, tool and mechanical structure

N = 1575 rpm 　　N = 2005 rpm

The lower speed is selected, that is, 1575 rpm

The influence of the rapid movement acceleration and deceleration of the tool holder

Calculation of the entry point and the exit point

(Calculation of incomplete teeth) Minimum entry distance L1

L1 = (tooth pitch P) * (spindle speed S) / 500

L1 = 2.54*1575/500=8.00mm

Minimum exit distance L2

L2 = (tooth pitch P) * (spindle speed S) / 2000

L2 = 2.54*1575/2000=2.00mm

Tooth depth and tooth bottom diameter d Tooth depth diameter d = nominal outer diameter D-2*h =19.05-2*1.65 = 15.75mm

Summary

Through the above-mentioned metric, imperial, and American thread calculation formulas, we can clearly see the uniqueness of each thread type in the calculation of tooth type, size, etc. Metric threads are widely used in the international industrial field with their simple standardization system; imperial threads still occupy an important position in some traditional machinery manufacturing due to their historical heritage and specific industry habits; American threads play a key role in related equipment based on the local industrial standards of the United States. Mastering these calculation formulas will not only help with precise operations in mechanical design, manufacturing, maintenance and other aspects, but also transcend different standard systems, achieve seamless global industrial cooperation and exchanges, and help the industrial field continuously move towards a higher and more advanced stage of development.