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# Design Of Metal Springs - Basics

## Video: Design Of Metal Springs - Basics

Metal springs are elements that deform in a targeted manner under load and return to their original shape when relieved. The energy supplied is converted into spring work (W) and released again at a later point in time (energy storage). However, the metal springs only reliably perform this deformation and energy absorption within the limits designed for them. Therefore, the correct spring design and spring calculation is an important component for the perfectly working metal spring.

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## The spring characteristic

Metal springs or technical springs are assessed according to their characteristic. This spring characteristic shows the dependence of the spring force (F) on the spring travel (s). Because depending on which spring characteristic is required (linear, progressive, degressive or combined), the shape and type of the spring also change.

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The spring characteristic in the spring diagram is determined with the spring rate (R). The spring rate (R) is therefore an important value when designing the right spring. With a linear spring characteristic, the spring rate is constant. Springs with a curved spring characteristic have a variable spring rate. The following formulas apply to a linear characteristic:

## for compression and tension springs

R = F2-F1 / s2-s1

## for leg and torsion springs

R M = M2-M1 / α2-α1

## The feather work

When the metal spring is tensioned, work is done, which is then released when the tension is released. The spring work (W) always results as the area below the spring characteristic.

With a linear spring characteristic, the following therefore applies:

W = ½F • s

## for torsion springs

W = ½M • α

By calculating the volume usage value, different types of springs can be compared using the ratio of spring work (W) and installation space (V):

η A = W / V

## The hysteresis

The suspension behavior can be influenced by external friction. These frictional forces prevent the spring from deforming. With alternating stress, this manifests itself in the form of a hysteresis loop. Part of the spring work is converted into heat by the friction and is then "lost". Since this is undesirable when using springs, any friction should be avoided constructively by the arrangement and shape of the springs.

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## The relaxation

For example, if a compression spring is compressed to a certain length between parallel plates at a higher temperature, it can be seen that the spring force gradually decreases over time. This loss of power increases with increasing temperature and voltage.

Relaxation of the material is a plastic deformation, which manifests itself as a loss of force with a constant installation length. This is given as a percentage based on the initial force F1:

Relaxation = ∆ F • 100 / F1

The relaxation values after 48 hours are used as characteristic values, although at this point the relaxation has not yet been completed. EN 13906-1 contains material-dependent relaxation diagrams. These are only to be included by the designer if high demands are placed on the constancy of the spring force.

The relaxation at different temperature states is also shown in the calculation in the spring calculation program WinFSB from Gutekunst Federn.

## The right choice of materials

Metal springs must be made of a suitable material and designed and designed so that they return to their original shape after a load has been removed.

This property is expressed in the elastic modulus and in the sliding modulus. These material parameters express the relationship between tension and elongation and should have the highest possible value.

• high elastic limits, ie have a large purely elastic range,
• endure the corresponding stresses even at elevated temperatures without major loss of force (low relaxation),
• have a high fatigue strength (fine-grained structure, free of impurities),
• have sufficient deformability,
• have as smooth a surface as possible,
• meet certain requirements for corrosion protection,
• be electrically conductive or non-magnetic.

## Increased working temperatures

The level of the working temperature can significantly influence the function of a spring, since the tendency to relax increases with increasing temperature. After evaluating the relaxation diagrams, certain limit temperatures for the minimum relaxation can be set for the most important spring materials.

## Use spring systems

For design reasons, it is also possible to use several springs to absorb forces and movements. Simple spring systems are parallel and series connections. (see fig. p. 29 below)

### a) Parallel connection

The springs are arranged in such a way that the external load (F) is divided proportionally among the individual springs, but the path of the individual springs can still be the same:

s = s1 = s2 = s3 =… (total suspension travel)

F = F1 = F2 = F3 =… (total spring force)

R = R1 + R2 + R3 =… (total spring rate)

The spring rate of the overall system of a parallel connection is always greater than the spring rate of the individual springs.

### b) Series connection

The springs are arranged one behind the other, so that the same force acts on each spring, but the travel is divided between the individual springs. The result is:

s = s1 = s2 = s3 =… (total suspension travel)

F = F1 = F2 = F3 =… (total spring force)

R = 1/1 / R1 + 1 / R2 + 1 / R3 +… (total spring rate)

The spring rate of the overall system of a series connection is always lower than the spring rate of the individual springs.

### c) mixing circuit

Several springs are connected in parallel and in series. Because of the balance, R1 = R2 and R3 = R4 must be. In the case shown:

R = 1/1 / (R1 + R2) + 1 / (R3 + R4) +… (total spring rate)

The spring rate of the overall system of the mixing circuit shown lies between the smallest and the largest spring rate of the individual springs.

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