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.
\( G=\dfrac {E}{2(1+ν)}\)
\(k=\dfrac {\ Gd^{4}}{8n_{w}D_{m}^{3}}\)
\( v_{(F)}=\dfrac {\ 8Fn_{w}D_{m}^{3}} {Gd^{4}} \)
\( v_{max}=\dfrac {\ n_{w}D_{m}^{2}πτ} {Gd} \)
\(τ_{(F)}=\dfrac {\ 8FD_{m}} {πd^{3}} \)