Spring Constant

Written by Jerry Ratzlaff on . Posted in Constants

spring compression 6Spring force constant, abbreviated as \(k_s\), also called spring constant, is the ratio of opposing force to the displacement from the origional position or how much force is needed to change a springs distance.

 

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Spring Constant formulas

\(\large{ k_s = - F \; d_s }\)   
\(\large{ k_s = \frac {F} {d_s} }\)   
\(\large{ k_s = \frac {2 \; E}{ d^2 } }\)   
\(\large{ k_s = \frac { F }{ x \;-\; x_0 } }\)  
\(\large{ k_s = \frac { 2 \; PE_s }{ x^2 } }\)  
\(\large{ k_s = \frac {G \; d^4} {8 \; n_a \; D^3} }\)   
\(\large{ k_s = \frac { 2 \; C \;+\; 1 }{ 2 \; C } }\)     \(\large{ C = \frac{ D }{ d_w } }\)  

Where:

 Units English Metric
\(\large{ k_s }\) = spring force constant \(\large{lbf}\) \(\large{N}\)
\(\large{ x }\) = distance from equilibrium \(\large{in}\) \(\large{mm}\)
\(\large{ D }\) = mean coil diameter \(\large{in}\) \(\large{mm}\)
\(\large{ n_a }\) = number of active coils \(\large{dimensionless}\)
\(\large{ G }\) = shear modulus of material \(\large{\frac{lbf}{in^2}}\) \(\large{Pa}\)
\(\large{ d_s }\) = spring displacement \(\large{in}\) \(\large{mm}\)
\(\large{ E }\) = spring energy \(\large{lbf-ft}\) \(\large{J}\)
\(\large{ F }\) = spring force \(\large{lbf}\)  \(\large{N}\)
\(\large{ x_0 }\) = spring equilibrium position \(\large{in}\) \(\large{mm}\)
\(\large{ PE_s }\) = spring potential energy \(\large{lbf-ft}\)  \(\large{J}\)
\(\large{ d_w }\) = wire diameter \(\large{in}\) \(\large{mm}\)
\(\large{ d }\) = wire size \(\large{in}\) \(\large{mm}\)

\(\large{ D/N }\) = index correction

  •  \(\large{ G }\) value for common spring materials
    • Copper = 6.5 x 10^6
    • Beryllium Copper = 6.9 x 10^6
    • Inconel = 11.5 x 10^6
    • Monel = 9.6 x 10^6
    • Music Wire = 11.5 x 10^6
    • Phospher Bronze = 5.9 x 10^6
    • Stainless Steel = 11.2 x 10^6
\(\large{dimensionless}\)

 

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Tags: Force Equations Constant Equations Spring Equations