Any material subject to the action of a load (force) is affected on a structural level through microscopic variations in geometry. Without wanting to discuss solid state physics, we can simplify by stating that when material is subject to load, stress is generated which we can define σ. Construction science has provided the knowledge necessary to estimate effort, based on the following factors.

  • Physical properties of the material.
  • Geometric characteristics of the material.
  • Type of stress.


Physical properties of the material

In the case of compression springs, the material is subject to torsion, this means that the modulus of elasticity is not E (Young’s modulus), valid for traction and compression stresses, but G (torsional modulus of elasticity). Furthermore, the stress is tangential to the section and not orthogonal. So technically it is not called σ but τ (tau).

As mentioned above, E and therefore G are typical of each material and represent the physical properties of the material. Both are the size of a pressure and are measured in Mpa (mega Pascal, 106 Pascal). Let’s see some typical values ​​for the most used materials in the elastic field.

Carbon steel: 81.500 Mpa.

Stainless steel 1.4310: 73,000 Mpa.

Cr Si alloy steel: 79.500 Mpa.

Phosphor Bronze: 42-44.000 Mpa.


Geometric characteristics of the material

The geometric factors that contribute to defining the stress are the wire diameter, the average winding diameter, and the number of coils.


Type of stress

The stress is obviously proportional to the compression length. So in the elastic field (remember Hooke’s law), the stress is a linear function of the working height. The more compression, greater the stress.

At this stage we begin to consider a factor that goes beyond the geometry of the spring, and which instead comes from experience and studies on materials. This factor is the number of compression cycles.

Usually, the spring is inserted in the application that uses it, in a state of pre-charge (compression at L1). Subsequently, it is activated (further compressed at L2), a complete actuation cycle is defined, the outward journey from L1 to L2 and return to L1.

Static application is considered if the number of cycles is less than 10,000, over the entire life span of the spring.

In this case the considerations made on the breaking load are valid, i.e. the spring breaks if compressing it, not only deform it but locally exceed the breaking load in the wire section.

It often happens that the geometry of the spring prevents the breaking load from being reached. In fact, there is not a sufficient stroke to induce a torsional state in the yarn that leads to breakage.

Therefore, for compression springs in static regime, the stress occurs in the worst configuration (dimension L2) and if this is lower than the safety limits the spring will not break, at least for factors attributable to the mechanics of the spring.

When we pass 10,000 cycles and start thinking in terms of 105 – 106 – 107 cycles and beyond, we enter the dynamic stress regime.

The formula used to calculate the static stress is no longer valid, or rather it must be corrected with a factor K, which increases the value under the same conditions. That is, at a fixed height the τ d > τ s, where d stands for dynamic and s stands for static.

It has been observed that under dynamic conditions, the stress state does not have a uniform distribution on the wire section. The stress increases near the inner surface of the coil, the K factor takes this into account. This factor depends on the winding ratio c, that is, on the ratio between the average diameter and the wire diameter. The lower the c, the greater the K factor.

There are several formulas for calculating K, the most used is K = (4c-1) / (4c-4)) + (0,615 / c).

This explains why the theoretical stress changes when considering a static or dynamic use of the spring.

As an example, we report the photograph of the section of a wire of a broken spring, you can see that the trigger at break occurred on the surface of the wire inside the winding.

Sezione filo molla rotta

Broken spring wire section

We conclude by saying that for each material the admissible stress is defined, as a percentage of the breaking load (Rm). This coefficient varies from material to material, and changes if the spring undergoes pre-yielding or not.

A good designer must first make sure that the theoretical stress at the most demanding workload is lower than the admissible stress.