Tension Springs - Nomenclature

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:

  • d < 17 mm
  • D ≤ 160 mm
  • n ≥ 3
  • 4 ≤ w ≤ 20

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

αb

-

Static security factor (loops)

 
αF

-

fatigue life factor (body)

 

r

Kg/dm3

Density

 
τ0

N/mm2

Initial stress (DIN Standard)

τ0 = (7.5 - 0.375 w) Rm / 100

τk2

N/mm2

Corrected stress related to F2

τk2= 8 k D F2 / ( p d3 )

τzul

N/mm2

Maximal allowable corrected stress

 




Manuel Paredes