Page 1178 - MiSUMi 2025

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

3.3.3 Spring Material Diameter 4.1.6 The spring mean diameter is calculated according to Formula (9).
The spring material diameter d is calculated by Formula (8) and should 4.1.7 Effective Number of Coils of Spring
be generally complied with GB/T 1358-2009 series. n= Gd 4 f EEEEEEEEEEEEEEEEEEE (25)
8D 3 (F─F0)
14 3.3.4 Spring Diameter 4.1.8 Deflection Energy
a) Spring Mean Diameter:
D = D1 + D2 EEEEEEEEEEEEEEEEEEEEEE (14) U = (F+F0) f EEEEEEEEEEEEEEEEEEEEE (26)
1
2
2
b) Spring I.D.: 4.2 Spring Characteristics and Deflection
Springs D1 = D ─ d EEEEEEEEEEEEEEEEEEEEEEE(15) 4.2.1 Spring Characteristics
c) Spring O.D.:
The design calculation is the same as that of cylindrical spiral compression springs.
D2 = D + d EEEEEEEEEEEEEEEEEEEEEEE(16)
The spring mean diameter D should be generally complied with the GB/T 1358- 4.2.2 Test Load
The design calculation is the same as that of cylindrical spiral compression springs.
2009 series, and the deviation value can be selected according to GB/T 1239.2- 4.2.3 Initial Tension
2009 and GB/T 23934-2015. In order to ensure sufficient installation space, the The close coil tension spring made of materials that do not need
Round Wire Coil Springs a) When both ends of the spring are fixed, from the free height to tightening, the which is called the initial tension F0. When the applied load exceeds the
increase in diameter of the spring under load should be considered.
quenching and annealing forms an axial pressure between the coils,
increase in the mean diameter is calculated according to the approximate formula (17):
initial tension, the spring begins to deform. After coiling and forming,

t 2 ─ d 2
EEEEEEEEEEEEEEEEEE (17)
Δ D =0.05
D
The initial tension is calculated according to Formula (27):
P.14-004 b) When the two end faces and the supporting seat can rotate freely and the friction is small, springs that need to be quenched and annealed have no initial tension.
πd 3
the increase in the mean diameter is calculated according to the approximate formula (18): F0 = 8D τ0 EEEEEEEEEEEEEEEEEEEEE (27)
t 2 ─ 0.8td ─ 0.2d 2

Tension Springs 3.3.5 Number of Coils of Spring EEEEEEEEEEEEEEE(18) In the formula, τ 0 is the initial tangential stress. For the steel spring, its value
Δ D =0.1
D
can also be selected in the shaded part of Figure 1 according to the winding
3.3.5.1 The effective number of coils of spring is calculated by Formula (10) and should
initial tension of the spring will decrease after treatment. In order to facilitate
be generally complied with the provisions of GB/T 1358-2009. In order to avoid ratio C. As the spring generally needs stress relief annealing treatment, the
P.14-016 excessive additional forces due to load eccentricity, and to ensure stable stiffness, manufacturing, it is recommended to take the lower limit value.
At the same time, its value can also be calculated by referring to
there are generally no less than 3 coils and at least no less than 2 coils.
Posts For Tension Springs 3.3.5.2 The supporting coil n z is related to the structural type of the end empirical formula (28):
coil, and the value of n z is shown in Table 2.
G
τ0 =
EEEEEEEEEEEEEEEEEEEEEE (28)
100C
3.3.5.3 Total Number of Coils
220
The mantissa should be 1/4, 1/2, 3/4 or the whole coil, and 1/2 coil is recommended.
P.14-020 n 1 =n +n z EEEEEEEEEEEEEEEEEEEEEEE(19) 200
3.3.6 Spring Free Height 180
Torsion Springs the exact value and its approximate value is calculated according to the formula 160
3.3.6.1 The free height H 0 is affected by the end structure, so it is difficult to calculate
listed in Table 4, as recommended to follow the provisions of GB/T 1358-2009.
Table 4 140
120
Pitch t
P.14-022 Total Number of Coils n 1 Free Height H 0 (H 0-d)/n End Structure Type Initial Tangential Stress τ0 /MPa 100
nt+d
n+1.5
Disc Springs n+2.5 nt+1.5d (H 0-1.5d)/n Both end coils 80
Both end coils
n+2
grinding
nt+2d
(H 0- 2d)/n
60
nt+3d
(H 0-3d)/n
n+2
n+2.5
P.14-023 3.3.6.2 Solid Height nt+3.5d (H 0-3.5 d)/n not grinding 40
20
The solid height of the spring is not specified in principle.
a) For a spring with 3/4 coil of end face grinding, when it is necessary to 0 3 4 5 6 7 8 9 10 11 12 13 14 15 16
specify the solid height, it is calculated according to Formula (20): C=D/d
H b ≤ n 1d max EEEEEEEEEEEEEEEEEEEEE(20) Figure 1 Relationship Diagram Between Winding Ratio and Initial Tangential Stress
b) For a spring without grinding at both ends, when it is necessary to F2 (Fs)
specify the solid height, it is calculated according to Formula (21): 4.2.4 Spring Working Drawing (See Figure 2) F1
F0
H b ≤(n 1+1.5)d max EEEEEEEEEEEEEEEEEE (21) H1
Where: H2
d max ---Maximum Material Diameter (Material Diameter + (Hs)
Maximum Limit Deviation), in millimeter (mm). (h2)
4 Design Calculation of Cylindrical Helical Tension Spring
4.1 Basic Calculation Formula
When there is no initial tension, the basic calculation formula of the tension spring is
the same as that of coil springs, calculated according to Formula (2) to Formula (11). h1 H0 d
When there is initial tension, the basic calculation of the tension spring is
calculated according to Formula (22) to Formula (26). a) With Initial Tension (Fs)
4.1.1 Spring Load F1 F2
Gd 4
F = f+F0 EEEEEEEEEEEEEEEEEEEE(22)
8D 3 n H1
H2
4.1.2 Spring Deflection (Hs)
f = 8D 3 n (h2)
Gd 4 (F─F0) EEEEEEEEEEEEEEEEEEE(23)
4.1.3 Spring Stiffness
Gd 4
F' = F ─ F0 = 8D 3 n EEEEEEEEEEEEEEEEEE (24)
f
h1 H0 d
4.1.4 The spring Torsional Stress is calculated according to Formula (5) or Formula (6).
b) Without Initial Tension
14-015 4.1.5 The spring material diameter is calculated according to Formula (8). Figure 2 Tension Spring Working Drawing 14-016