Compression spring formulas including spring index formula, Wahl factor formula, spring rate formula, shear stress at spring body formula,
spring outer diameter at solid height formula, spring stability condition and Hooke's law.
|
Parameter |
Formula |
|
Spring outer diameter [OD] |
OD = D + d |
|
Spring inner diameter [ID] |
ID = D - d |
|
Spring index [C] |
C = D/d |
|
Wahl factor [Kw] |
$${ K }_{ W }=\frac { 4C-1 }{ 4C-4 } +\frac { 0.615 }{ C } $$ |
|
Shear stress
at spring body (corrected with Wahl factor)- used for unprestressed springs [τs] |
$$\tau ={ K }_{ W }\frac { 8FD }{ \pi { d }^{ 3 } } $$ |
|
Shear stress
at spring body (uncorrected )- used for prestressed springs [τs] |
$$\tau =\frac { 2C+1 }{ 2C } \times \frac { 8FD }{ \pi { d }^{ 3 } } $$ |
|
Spring rate [k] |
$$k=\frac { { d }^{ 4 }G }{ 8{ D }^{ 3 }{ N }_{ a } } $$ |
|
OD at solid height [ODat solid] |
$${ OD }_{ at\quad solid }=\sqrt { { D }^{ 2 }+\frac { { p }^{ 2 }-{ d }^{ 2 }
}{ { \pi }^{ 2 } } } +d$$ |
|
Spring stability condition |
$${ L }_{ f }<\frac { \pi D }{ \alpha } { \left[ \frac { 2(E-G) }{ 2G+E }
\right] }^{ 1/2 }$$ |
|
Hooke's Law |
$$\Delta F=k\Delta x$$ |