Tension spring
Contrary to the compression springs, the traction springs have a theoretical characteristic which does not pass by the null load. There exists an initial tension, the spring is prestressed.
DIN standards detail the validity range for the formulae: basic formulae for tension springs Symbol Unit Detail Formula AL0 mm tolerance on free length D mm Mean diameter D = De - d De mm External diameter De = D + d Di mm Internal diameter Di = D - d d mm Wire diameter d = De-D E N/mm2 Elastic modulus F0 N Initial load F0 = π d3 τ0 / ( 8 D ) F1, F2 N Loads related to L1, L2 F1 = F0 + R (L1 - L0) F2 = F0 + R (L2 - L0) Fn N Load related to τzul Fn = τzul π d3 / ( 8 D k ) G N/mm2 Torsion modulus k - stress correction factor k = ( w + 0.5 ) / ( w - 0.75 ) L0 mm Free length L0 = 2 Di + n (d +1) L1, L2 mm Operating lengths L1 = L0 + (F1 - F0) / R L2 = L0 + (F2 - F0) / R L1I mm Minimal operating length L2S mm Maximal operating length Ln mm Maximal allowable length Ln = L0 + (Fn - F0) / R M g Spring mass M = r D π2 d2 (n + 2) / 4000 N - Number of cycles n - Number of active coils n = G d4 / ( 8 R D3 ) nt - Total number of coils nt = n + 2 R N/mm Spring rate R = G d4 / ( 8 n D3 ) Rm N/mm2 Ultimate Tensile Strength Sh mm Spring travel Sh = L2 - L1 W Nmm Energy W = 0.5 (F1 + F2) (L2-L1) w - spring index w = D/d - Static security factor (loops) - fatigue life factor (body) r Kg/dm3 Density N/mm2 Initial stress (DIN Standard) τ0 = (7.5 - 0.375 w) Rm / 100 N/mm2 Corrected stress related to F2 τk2= 8 k D F2 / ( p d3 ) N/mm2 Maximal allowable corrected stress
αb
αF
τ0
τk2
τzul