Parallel Systems of Springs of Various Stiffness

In upholstered furniture, there are several construction solutions used for spring units, which constitute the main spring layer. Biconical springs and cylindrical springs (Fig. 8.33a, b) are used in many designs of mattresses. However, the latest solutions tend towards a serial or parallel connection of springs of varying geometry (Fig. 8.33c). Such a compilation of springs enables to obtain nonlinear character­istics of deformations of spring systems of upholstered furniture and also to match the stiffness of the bed to the individual needs of the user.

The analysis of the softness of spring systems in upholstered furniture proves that these layers, from an engineering point of view, should consist of elements of nonlinear and progressive compression characteristics. It is more favourable to use biconical springs for this purpose, in which the progressive characteristics of operation are caused by the settling of coils (Fig. 8.34a).

However, they do not always meet the expectations of the designer, especially when he is looking for an element with a precisely calculated variable of stiffness, which can ensure high softness of the system in places of weak load of the user’s body, and at the same time a large hardness in places of strong stresses. The spring, which could meet these requirements, should consist of a minimum of two ele­mentary springs connected in parallel (Fig. 8.34b).

The compression characteristics of the entire system kz will then consist of sections representing the deformation of element k1 until its settling on limiters, a base or another element of k2 stiffness, and joint stiffness of both components kz = k1 + k2. It is important in this case to determine such stiffnesses k1 and k2, respectively, for the larger and smaller spring, which will correspond to stresses of the human body placed at a given point of the seat or bed surface.

A study of the phenomenon of settling of coils in parallel inserts of cylindrical springs can be carried out using numerical methods. Figure 8.35 shows a mesh model of a fragment of a spring unit, consisting of two cylindrical springs, of the dimensions: diameter 60 mm, height 125 mm, diameter 26 mm, height 100 mm. The model has been made from six – to eight-node isotropic solid elements. In order

Fig. 8.33 Upholstery springs: a biconical, b cylindrical, c double system of cylindrical springs

to mark the settling of coils of the shorter spring on a stiff base, it has been supported by gap-type elements. Thanks to them, a case of individual compression has been observed in the larger spring, and after exhausting the height hp (Fig. 8.34), simultaneous compression of both springs. In the first load scheme, the force 3 N was used. This value was to guarantee that a spring of 60 mm in diameter and k1 stiffness will deform in a controlled manner, and the value of this dis­placement will amount to!1 = P1/k1 = 25 mm. As it can be seen in Fig. 8.36, the simulation brought the intended effect. The displacement amounted to 25 mm, and the spring of 26 mm in diameter set its base on an unmovable support.

In the second calculation scheme, the model was loaded by a force of 38 N. This value derives from the studies of stresses of the human body, lying down in a lateral position, on a mattress of spring construction. When calculating the deformation of the springs system of alternative stiffness kz = 0.62 N/mm, the displacement value that should have been expected was at the level X2 = P2/kz = 61.1 mm. As shown in Fig. 8.37, the displacement value marked numerically amounted to almost 61.1 mm. This means that the developed model correctly reflects the nature of work of parallel systems of springs subjected to compression. Therefore, modelling mattresses

systems of furniture for lying down, containing complex spring systems, should not pose too many problems, and the results of the calculations will correspond to real values. In this context, any mattress can be designed which characteristics of stiff­ness will result not only from applying the right stiffness of springs connected in parallel, but also foams and rubbers combined with springs in serial systems.