METRIC THREAD PROFILE FORM FORMULAS

Metric thread profile is defined in ISO 68-1 standard.

The basic profile for ISO general purpose metric screw threads

ISO metric screw thread basic profile according to ISO 68-1

Metric thread root form is defined in ISO 965-1 standard.

Root contour for ISO general purpose metric screw threads

ISO metric screw external thread root contour according to ISO 965-1 for positions e, f, g

Metric Thread Formulas:

Parameter Equation
Height of fundamental triangle [H] $$H=\frac { \sqrt { 3 } }{ 2 } P$$
Thread basic pitch diameter [d2 , D2] $${ d }_{ 2 }={ D }_{ 2 }=d-2\times \frac { 3 }{ 8 } H=D-2\times \frac { 3 }{ 8 } H$$
Thread basic minor diameter [d1 , D1 ] $${ d }_{ 1 }={ D }_{ 1 }=d-2\times \frac { 5 }{ 8 } H=D-2\times \frac { 5 }{ 8 } H$$
External thread minimum truncation [Cmin] $${ C }_{ min }=0.125P$$
External thread maximum truncation [Cmax] $${ C }_{ max }=\frac { H }{ 4 } -{ R }_{ min }\left\{ 1-\cos { \left[ \frac { \pi }{ 3 } -\arccos { \left( 1-\frac { { T }_{ d2 } }{ 4{ R }_{ min } } \right) } \right] } \right\} +\frac { { T }_{ d2 } }{ 2 }$$
External thread maximum major diameter [dmax] $${ d }_{ max }=d+es$$
External thread minimum major diameter [dmin] $${ d }_{ min }={ d }_{ max }-{ T }_{ d }$$
External thread maximum pitch diameter [d2max] $${ d }_{ 2max }={ d }_{ 2 }+es$$
External thread minimum pitch diameter [d2min] $${ d }_{ 2min }={ d }_{ 2max }-{ T }_{ d2 }$$
External thread maximum minor diameter [d3max] $${ d }_{ 3max }={ d }_{ 1 }-es-2y$$
External thread minimum minor diameter [d3min] $${ d }_{ 3min }={ d }_{ 1 }-es-2z$$
Dimension y $$y={ R }_{ min }\left\{ 1-\cos { \left[ \frac { \pi }{ 3 } -\arccos { \left( 1-\frac { { T }_{ d2 } }{ 4{ R }_{ min } } \right) } \right] } \right\} $$
Dimension z $$z=\frac { H }{ 4 } +\frac { { T }_{ { d }_{ 2 } } }{ 2 } -\frac { P }{ 8 }$$
Internal thread minimum major diameter [Dmin] $${ D }_{ min }=D+EI$$
Internal thread maximum pitch diameter [D2max] $${ D }_{ 2max }={ D }_{ 2min }+{ T }_{ D2 }$$
Internal thread minimum pitch diameter [D2min] $${ D }_{ 2min }={ D }_{ 2 }+EI$$
Internal thread maximum minor diameter [D1max] $${ D }_{ 1max }={ D }_{ 1min }+{ T }_{ D1 }$$
Internal thread minimum minor diameter [D1min] $${ D }_{ 1min }={ D }_{ 1 }+EI$$

Note: es, EI- Fundamental deviation, Td-Major diameter tolerance of external thread,Td2-Pitch diameter tolerance of external thread,TD1-Minor diameter tolerance of internal thread, TD2-Pitch diameter tolerance of internal thread

Supplements:

Reference:

  • Oberg, E. , Jones ,F.D. , Horton H.L. , Ryffel H.H., (2016) . Machinery's Handbook . 30th edition.  Industrial Press Inc.
  • Oberg, E. , Jones ,F.D. , Horton H.L. , Ryffel H.H., (2012) . Machinery's Handbook . 29th edition.  Industrial Press Inc.
  • ASME B1.5-1997, ACME Screw Threads