Compression Spring

Written by Jerry Ratzlaff on . Posted in Fastener

spring compression 1

A compression spring is a open-coil helical springs wound to resist the compression force along the wind axis.  The spring will always resist and pushing back the compression force to its origional length.

 

 

 

 

 

 

spring compression 7Compression Spring Deflection formula

\(\large{ d_s = \frac{  64 \; n_a \; r^3 \; F  }{ d^4 \; G }  }\)

Where:

\(\large{ d_s }\) = spring deflection

\(\large{ n_a }\) = number of active coils

\(\large{ G }\) = shear modulus of material

\(\large{ F }\) = spring force

\(\large{ r }\) = spring radius  ( \(\large{ \frac{D}{2} }\) )

spring compression 11\(\large{ d }\) = wire diameter

Compression Spring Diameter formula

\(\large{ D = D_o - d  }\)

\(\large{ D = D_i + d  }\)

Where:

\(\large{ D }\) = mean coil diameter

\(\large{ D_i }\) = inside diameter

\(\large{ D_o }\) = outside diameter

\(\large{ d }\) = wire diameter

Solve for:

\(\large{ D_i = D_o - 2 \; d  }\)

\(\large{ D_o = D_i + 2 \; d  }\)

Compression Spring Force formula

\(\large{ F = \frac{ \pi }{ 16 } \; \frac{ d_{s}{^3} }{ r }  \; \tau }\)

Where:

\(\large{ F }\) = spring force

\(\large{ d_s }\) = spring deflection

\(\large{ \pi }\) = Pi

\(\large{ \tau }\) (Greek symbol tau) = shear stress

\(\large{ r }\) = spring radius  ( \(\large{ \frac{D}{2} }\) )

\(\large{ d }\) = wire diameter

Compression Spring index formula

\(\large{ C = \frac{ D }{ d }  }\)

Where:

\(\large{ C }\) = spring index

\(\large{ D }\) = mean coil diameter

\(\large{ d }\) = wire diameter

Compression Spring load when compressed to length formula

\(\large{ P =  T \; n_s   }\)

\(\large{ P = n_s \; \left( l_i - l_f  \right)  }\)

Where:

\(\large{ P }\) = load when compressed to length

\(\large{ l_f }\) = final length (compressed)

\(\large{ l_i }\) = initial length (free)

\(\large{ T }\) = travel length

\(\large{ n_s }\) = spring rate

Compression Spring Mean Coil Diameter formula

\(\large{ D = ID + d  }\)

Where:

\(\large{ D }\) = mean coil diameter

\(\large{ ID }\) = inside diameter

\(\large{ d }\) = wire diameter

Compression Spring Rate formula

\(\large{ n_s = \frac{ G \; d^4 }{ 8 \; n_a \; D^3 }  }\)

Where:

\(\large{ n_s }\) = spring rate

\(\large{ D }\) = mean coil diameter

\(\large{ n_a }\) = number of active coils

\(\large{ G }\) = shear modulus of material

\(\large{ d }\) = wire diameter

Compression Spring Solid Coils Height formula

\(\large{ h = d \; \left( n_t + 1 \right)  }\)

\(\large{ h = d \; n_t  }\)   (for ground ends)

Where:

\(\large{ h }\) = solid height

\(\large{ n_t }\) = total number of coils

\(\large{ d }\) = wire diameter

Compression Spring Travel length formula

\(\large{ T =  \frac{P}{n_s}  }\)

Where:

\(\large{ T }\) = travel length

\(\large{ P }\) = load when compressed to length

\(\large{ n_s }\) = spring rate

Compression Spring Wire Length formula

\(\large{ L_c = D \; \pi  }\)   (coil wire length)

\(\large{ L_t = L_c \; n_t  }\)   (total wire length)

Where:

\(\large{ L_c }\) = coil wire length

\(\large{ L_t }\) = total wire length

\(\large{ D }\) = mean coil diameter

\(\large{ \pi }\) = Pi

\(\large{ n_t }\) = total number of coils

Compression Spring Wire Stress formula

\(\large{ S = \frac{ 8 \; p \; D \; K }{ \pi \; d^3 }  }\)

\(\large{ S = \frac{ 8 \; n_s \; D \; K \; d_s }{ \pi \; d^3 }  }\)

Where:

\(\large{ S }\) = wire stress

\(\large{ D }\) = mean coil diameter

\(\large{ \pi }\) = Pi

\(\large{ p }\) = pitch

\(\large{ d_s }\) = spring deflection

\(\large{ n_s }\) = spring rate

\(\large{ K }\) = stress correction factor

\(\large{ d }\) = wire diameter

 

Tags: Equations for Spring