Page 1177 - MiSUMi 2025

Economy series
Technical Calculation Excerpted from GB/T 23935-2009 Springs

1 Parameter Names and Codes of Springs K in the formula is Stress Correction Factor (Wahl Factor), and the value of K is calculated according to Formula (7):
This standard uses the terms and symbols specified in GB/T 1805-2001 and Table 1. K= 4C─1 0.615 EEEEEEEEEEEEEEEEEEEEE(7)
+
Table 1 4C─4 C
Parameter Name Code Unit Under static load, the value of K can generally be taken as 1. When the spring stress is high, the value of K is also considered. 14
3.1.5 Spring Material Diameter:
Material Diameter d mm 8KDF 8KCF
d ≥ or d ≥ EEEEEEEEEEEEEEEE(8)
Spring I.D. D 1 mm π[τ] π[τ]
[τ] in the formula is the Allowable Torsional Stress determined according to the above design
Spring O.D. D 2 mm conditions.
Spring Mean Diameter D mm 3.1.6 Spring Mean Diameter: Springs
D=Cd EEEEEEEEEEEEEEEEEEEEEEEEE(9)
Total Number of Coils n1 Coils
Number of Supporting Coils nz Coils 3.1.7 Effective Number of Coils of Spring:
Gd 4
Effective Number of Coils n Coils n= 8D 3 F f EEEEEEEEEEEEEEEEEEEEEEE(10)
Free Height (Free Length) H0 mm 3.2. Natural Vibration Frequency
For the cylindrical helical coil springs with fixed ends and one end periodically reciprocating within Coil Springs Round Wire
Solid Height H b mm the working stroke range, its natural vibration frequency is calculated according to Formula (12):
Pitch t mm f e = 3.56d G
nD 2 EEEEEEEEEEEEEEEEEEEEE(12)
Load F 1,2,...n N ρ P.14-004
3.3 Spring Characteristics and Deflection
Stress Correction Factor (Wahl Factor) K ---
3.3.1 Spring Characteristics
Material Shear Modulus G MPa a) When it is necessary to ensure the load at the specified height, the Springs Tension
Torsional Stress τ1,2,...n MPa deflection of the spring shall be between 20% and 80% of the deflection
under the test load, i.e. 0.2 f s ≤ f 1, 2, ... n ≤ 0.8 f s .
Allowable Torsional Stress [τ] MPa b) When it is necessary to ensure the height under the load, the deflection
of the spring shall be between 20% and 80% of the deflection under the P.14-016
Initial Tension F 0 N
test load, i.e. 0.2 f s ≤ f 1, 2, ... n ≤ 0.8 f s , but the load under the maximum
deflection should be no greater than the test load.
2 Principle of Allowable Stress Selection c) When it is necessary to ensure the stiffness, the deflection of the spring
a) For springs under static load, in addition to considering strength shall be between 30% and 70% of the deflection under the test load, i.e. Tension Springs Posts For
conditions, if there are requirements for stress relaxation, the f 1 and f 2 meet the conditions of 0.3 f s ≤ f 1, 2 ≤ 0.7 f s . The spring stiffness is
allowable stress shall be appropriately reduced. calculated according to Formula (13):
b) For springs under dynamic load, in addition to the number of cycles, F2 ─ F1 F2 ─ F1 P.14-020
=
the stress (change) amplitude should also be considered, which F' = f 2 ─ f 1 H1 ─ H2 EEEEEEEEEEEEEEEEEEE (13)
is calculated according to the cycle characteristic formula (1), and 3.3.2 Spring End Structure Type
checked in Figure 2. When the cycle characteristic value is large, See Table 2 for the spring end structure type.
that is, the stress (change) amplitude is small, the allowable stress Table 2 Springs Torsion
is taken as the large value; and when the cycle characteristic value
is small, that is, the stress (change) amplitude is large, the allowable Shape Code Sketch End Structure Type
stress is taken as the small value. Both end coils tightened P.14-022
γ= τmin = F min or γ = σmin = T min = φ min EEEEEE(1) YI and grinding
nZ ≥ 2
τmax F max σmax T max φ max
c) For springs in important applications, where damage has a Both end coils tightened Disc Springs
significant impact on the entire machinery, and springs operating Cold Coil Compression Spring YII but not grinding
at higher or lower temperatures, the allowable stress should be nZ ≥ 2
reduced appropriately. Both end coils not P.14-023
d) The fatigue strength or fatigue life of the spring can be improved by YIII tightened
effective shot peening treatment. nZ < 2
e) For the coil springs, the fatigue life can be increased by effective Both end coils tightened
strong pressure treatment, which has obvious effect on improving RYI and grinding
the performance of the spring. nZ ≥ 1.5
f) There are many factors affecting the fatigue strength of springs
under dynamic load, which are difficult to estimate accurately. For Both end coils tightened
springs for important purposes, test verification should be carried out RYII but not grinding
after the design is completed. Hot Coil Compression Spring nZ ≥ 1.5
3 Design Calculation of Cylindrical Helical Coil Springs RYIII Both end coils flattened,
tightened and grinding
3.1 Basic Calculation Formula nZ ≥ 1.5
3.1.1 Spring Load: Both end coils flattened,
F= Gd 4 f EEEEEEEEEEEEEEEEEEEEE (2) RYIV tightened but not grinding
8D 3 n nZ ≥ 1.5
See Appendix A for the material shear modulus G in the formula.
3.1.2 Spring Deflection: Table 3 Shear Modulus of Elasticity(G)
8D 3 nF G Value N/mm 2
f = Gd 4 EEEEEEEEEEEEEEEEEEEEE (3) Material (kgf/mm 2 ) Symbol
3.1.3 Spring Stiffness: Spring Steel 78 × 10 3 {8 × 10 3 } SUP6, 7, 9, 9A, 10, 11A, 12, 13
F Gd 4 Hard Steel Wire 78 × 10 3 {8 × 10 3 } SW-B,SW-C
F' = f = 8D 3 n EEEEEEEEEEEEEEEEEEEE (4) Piano Wire 78 × 10 3 {8 × 10 3 } SWP
SWO, SWO-V, SWOC-V,
3.1.4 Spring Tangential Stress: Oil Tempered Steel Wire 78 × 10 3 {8 × 10 3 } SWOSC-V, SWOSM, SWOSC-B
πd 3 EEEEEEEEEEEEEEEEEEEEE (5)
τ =K 8DF SUS302 SUS302
SUS304
SUS304
or Stainless SUS304N1 69 × 10 3 {7 × 10 3 } SUS304N1
Gdf
τ=K πD 2 n EEEEEEEEEEEEEEEEEEEEE (6) Steel Wire
SUS316
SUS316
14-013 SUS631J1 74 × 10 3 {7.5 × 10 3 } SUS631J1 14-014