Helical spring with round cross section

Determine mechanical properties of a helical spring with wire diameter d, radius r, shear modulus G and nw as number of active windings. Calculate also deflection v and tension σ as a function of force F.

The shear modulus can be calculated using Young's Modulus and Poisson's ratio of a material.

\( G=\dfrac {E}{2(1+ν)}\)

F d D m r n w = 6

\(k=\dfrac {\ Gd^{4}}{8n_{w}D_{m}^{3}}\)

\( v_{(F)}=\dfrac {\ 8Fn_{w}D_{m}^{3}} {Gd^{4}} \)

\( v_{max}=\dfrac {\ n_{w}D_{m}^{2}πτ} {Gd} \)

\(τ_{(F)}=\dfrac {\ 8FD_{m}} {πd^{3}} \)