How the spring calculator works
A compression spring's rate depends on the wire's shear modulus and diameter, the coil diameter and the number of active coils. Stress concentrates on the inside of each coil, which the Wahl factor corrects for.
- Spring rate:
k = G·d⁴ / (8·D³·n) - Spring index:
C = D/d - Wahl factor:
K_W = (4C−1)/(4C−4) + 0.615/C - Shear stress:
τ = K_W·8·F·D / (π·d³)
Worked example: chrome-silicon valve spring
A spring of 4 mm chrome-silicon wire, 30 mm outside diameter and 6 active coils has a rate of about 23.4 N/mm. At 10 mm of deflection it carries about 234 N with a stress safety factor near 2.9, and it still has a safety factor of about 1.6 if compressed solid.
Good to know
- Keep the spring index between about 4 and 12, and stay out of the last 15% of travel before solid.
- Pro checks buckling for your end support and gives the natural frequency, so cyclic loading stays clear of surge.