Spiral wound spring with rectangular cross section

Determine mechanical properties of a spiral wound spring with blade width b, blade thickness h,radius r, Young's modulus E and L as spring length. Calculate also deflection v and tension σ as a function of force F.

F b v n w = 5 r h

\(k=\dfrac {\ Eb^{2}h^{2}}{12Lr^{2}}\)

\( v_{(F)}=\dfrac {\ 12FLr^{2}} {Eb^{2}h^{2}} \)

\( v_{max}=\dfrac {\ 2rLσ} {Eh} \)

\(σ_{(F)}=\dfrac {\ 6Fr} {hb^{2}} \)