Spring Constant
Spring 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 | \(\large{\frac{lbf}{in^2}}\) | \(\large{MPa}\) |
| \(\large{ d_s }\) = 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
|
\(\large{dimensionless}\) | |
Tags: Equations for Force Equations for Constant Equations for Spring