After determining the spring dimensions, the Proof of strength be guided. For this purpose, the existing shear stress is determined.

## Shear stress for compression springs

#### Shear stress compression spring from force:

\Large\tau=\frac{8DF}{\pi d^{3}}

#### Shear stress Compression spring from displacement:

\Large\tau=\frac{Gds}{\pi nD^{2}}

While the shear stress τ is to be used for the design of statically or quasi-statically loaded springs, the corrected shear stress τk applies for dynamically stressed springs. The distribution of shear stress in the wire cross-section of a spring is uneven, the highest stress occurs on the inside diameter of the spring. With the tension correction factor k, which depends on the winding ratio (ratio of mean diameter to wire thickness) of the spring, the highest tension can be approximately determined. For dynamically stressed springs we get:

#### Corrected shear stress compression spring:

\Large \tau_{{\kappa}}=\kappa\cdot\tau

where the following applies for k (according to Bergsträsser): \Large \kappa=\frac{\frac{D}{d}+0.5}{\frac{D}{d}-0.75}

Now the comparison is made with the permissible voltage. This is defined as follows:

#### Permissible tension of compression spring:

\Large \tau_{{zul}}=0.5\cdot R_{{m}}

or

\Large \tau_{{czul}}=0.56\cdot R_{{m}}

The values for the Minimum tensile strength Rm are dependent on the wire thickness and can be found in the standards of the corresponding materials.

As a rule, it must be possible to compress compression springs up to the block length, which is why the permissible stress for the block length is tczul to consider.

At dynamic stress must lower and upper voltage (tk1 and tk2) of the corresponding stroke can be determined. The difference is the stroke voltage. Both the upper tension and the stroke tension must not exceed the corresponding permissible values. These are the Fatigue strength diagrams of EN 13906-1: 2002 refer to. If the tensions stand up to this comparison, the spring is fatigue-resistant with a maximum number of load cycles of 10 7.

## Shear stress for tension springs

As with Compression spring calculations the existing shear stress is to be determined.

#### Shear stress:

\Large \tau=\frac{8DF}{\pi d^{3}}

The corrected stroke tension must also be calculated for dynamic loading (see Chapter 1.4.2.2).

#### Corrected shear stress :

\Large \tau_{{\kappa}}=\kappa\cdot\tau

#### Allowable voltage:

\Large \tau_{{zul}}=0.45 \cdot R_{{m}}

The existing maximum voltage tn for the largest travel sn is set equal to the permissible voltage. To however relaxation To avoid this, only 80% of this spring travel should be used in practice.

\Large s_{{2}}=0.8 \cdot s_{{n}}

No generally applicable fatigue strength values can be given for dynamic loads, as additional stresses can occur at the bending points of the eyelets, some of which can exceed the permissible stresses. Tension springs should therefore only be subjected to static loads if possible . If dynamic stress cannot be avoided, one should go for angled Eyelets do without and use rolled or screwed-in end pieces. A life test under later operating conditions makes sense. A Surface hardening by shot peening is not feasible because of the tight turns.

Explanation of symbols:
d = wire diameter (mm)
D = mean coil diameter (mm)
F = spring force (N)
G = shear modulus (N / mm²)
n = number of resilient coils (pieces)
Rm = minimum tensile strength (N / mm²)
s = spring deflection (mm)
τ = shear stress (N / mm²)
τzul = permissible shear stress (N / mm²)
τczul = permissible shear stress for block length (N / mm²)