Compression spring formulas for fatigue design.
|
Parameter |
Formula |
|
Force amplitude [Fa] |
Fa = (Fmax - Fmin)/2 |
|
Midrange force [Fm] |
Fm = (Fmax + Fmin)/2 |
|
Spring outer diameter [OD] |
OD = D + d |
|
Spring inner diameter [ID] |
ID = D - d |
|
Spring index [C] |
C = D/d |
|
Whal factor [Kw] |
$${ K }_{ W }=\frac { 4C-1 }{ 4C-4 } +\frac { 0.615 }{ C } $$ |
|
Shear stress amplitude [τa] |
$${ \tau }_{ a }={ K }_{ W }\frac { 8{ F }_{ a }D }{ \pi { d }^{ 3 } } $$ |
|
Midrange shear stress [τm] |
$${ \tau }_{ m }={ K }_{ W }\frac { 8{ F }_{ m }D }{ \pi { d }^{ 3 } } $$ |
|
Torsional rupture strength [Ssu] |
Ssu=0.67Sut |
|
Slope line [r] |
$$r=\frac { { \tau }_{ a } }{ { \tau }_{ m } } $$ |
|
Amplitude strength component for infinite life (Shot peened)-(Zimmerli Data) [Ssa_zim] |
Ssa = 398 MPa (57.5 kpsi) |
|
Midrange strength component for infinite life (Shot peened)-(Zimmerli Data) [Ssm_zim] |
Ssa = 534 MPa (77.5 kpsi) |
|
Amplitude strength component for infinite life (Unpeened)-(Zimmerli Data) [Ssa_zim] |
Ssa = 241 MPa (35 kpsi) |
|
Midrange strength component for infinite life (Unpeened)-(Zimmerli Data) [Ssm_zim] |
Ssa = 379 MPa (55 kpsi) |
|
Shear endurance limit according to Gerber (with Zimmerli Data) [Sse] |
$${ S }_{ se }=\frac { { S }_{ sa\_ zim } }{ 1-{ ({ S }_{ sm\_ zim }/{ S }_{ su
}) }^{ 2 } } $$ |
|
Shear stress amplitude limit (According to Gerber failure criteria) [Ssa] |
$${ S }_{ sa\_ lim }=\frac { { r }^{ 2 }{ S }_{ su }^{ 2 } }{ 2{ S }_{ se } }
[-1+\sqrt { 1+{ (\frac { 2{ S }_{ se } }{ r{ S }_{ su } } ) }^{ 2 } } ]$$ |
|
Shear endurance limit according to Goodman (with Zimmerli Data) [Sse] |
$${ S }_{ se }=\frac { { S }_{ sa\_ zim } }{ 1-({ S }_{ sm\_ zim }/{ S }_{ su })
}$$ |
|
Shear stress amplitude limit (According to Goodman failure criteria) [Ssa] |
$${ S }_{ sa\_ lim }=\frac { r{ S }_{ se }{ S }_{ su } }{ r{ S }_{ su }{ S }_{
se } } $$ |
|
Shear stress amplitude limit (According to Sines failure criteria) [Ssa] |
Ssa_lim = Ssa_zim |
|
Factor of safety against fatigue [fosf] |
$${ fos }_{ f }=\frac { { S }_{ sa\_ lim } }{ { \tau }_{ a } } $$ |