DESIGN OPTIMISATION OF SPRINGS AND SEALS BY MEANS OF FINITE ELEMENT SIMULATIONS

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1 DESIGN OPTIMISATION OF SPRINGS AND SEALS BY MEANS OF Yasar Deger HSR, University of Applied Sciences Rapperswil, Switzerland SUMMARY The use of FE analysis can help to better understand the deformation behaviour of the springs and seals and to develop customised ones according to the specifications of an end product. The mechanical behaviour of springs e.g. varies significantly depending on the direction and loading level and exhibit not seldom complex nonlinearities. It is possible to influence these characteristics not only by the choice of materials but also by proper modifications of the shape and mounting details. Two different components are presented and discussed in this paper to show the work performed for two different industrial partners within the framework of technology transfer activities: An elastomer seal of a small piston for domestic appliances and a steel spring for mounting of light bulbs, produced for lorries. Both components have the common property that they are subject to large displacements. The elastomer seal of extremely small size is undergoing large strains under rather static operational conditions, while the contact pressure should be maintained relatively continuous for tightness reasons, even when the geometry slightly differs from an axisymmetric one. excentric. The design of the steel spring had to be re-analysed in order to find out the reason of cracks occurring occasionally in a certain position. For the elastomer seal the material behaviour has been analysed in a first step by means of laboratory tests on rubber specimens. Based on these data it has been described later on using Ogden type material model and experimental data fit option of the FE software. With 2D and 3D nonlinear calculations on FE models of the original seal and of its alternatives it was tried to find out the best solution for leak tightness without reaching high stress levels. In the case of steel spring, the failure mechanism could be clarified firstly and then a series of geometric parameters and mounting details were selected and investigated by means of sensitivity analyses focusing on their influence on the stress concentrations. Subsequently, proposals have been worked out in a step by step approach to enhance the design of the mentioned products in close cooperation with the project partners. Similar investigations can be performed in a relatively straight forward manner in order to optimise the design of any other component significantly.

2 1: FE modelling and analysis of an elastomer seal An axisymmetric component consisting of hyperelastic material can easily exhibit significant non-axisymmetric deformations due to imperfections of operational conditions, which can cause tightness problems if the component should act as a seal. Aiming to analyse possible deviation ranges of the contact pressure related to excentricity tolerances of the production, a series of finite element simulations has been performed recently for an elastomer seal of a small piston device for domestic appliances. In a first step the material behaviour has been measured by means of laboratory tension tests on a number of specimens (Fig. 1). Subsequently, an appropriate material behaviour description has been obtained by means of the experimental data fitting features of the FE software and verified on a simple model by means of a comparison with the real test data (Fig. 2). The nonlinear analysis, performed then using a 2D FE model of the seal under ideal i.e. perfectly symmetric mounting and operational loading conditions for reference purposes has shown its typical deformation behaviour and stress / contact pressure levels to be expected (Fig. 3). This model consisted of axisymmetric solids (2D Hermann elements) and surfaces. 1.2 Cauchy Stress [MPa] Strain Figure 1: Typical stress-strain curve of the hyperelastic seal material.

3 Figure 2: A very simple FE model can allow to reproduce the force-displacementor stress-strain-curve, measured on the specimen, upon activation of a proper material model (e.g. of the type Ogden). Figure 3: Comparison of the 2D FE model, deformed under the influence of contacting rigid surfaces, with its original shape.

4 In order to simulate a possible imperfection (e.g. due to improper mounting of the seal into the piston device) a 3D FE model has been created using the same hyperelastic material behaviour. This model with rotational symmetry was then subject to forced displacements within slightly excentric contact surfaces. The results could be evaluated in terms of contact pressure and maximum principal stress. It is interesting to note that according to the plots - only a percentage of millimetre is enough to cause leakage due to interruptions of the contact pressure (Fig. 4). The contact pressure within specified ranges is, of course, of crucial importance for the tightness of the piston operation. Further FE analyses with some minor geometric modifications of the seal (e.g. change of the radius of curvatures and/or of thicknesses) could enable to ensure that it is possible to maintain a minimum quantifiable contact pressure for a certain excentricity of the inner and outer contact surfaces. Another possibility to further enhance the fulfilment of contact requirements would be to select a material with slightly different deformation characteristics. Figure 4: The analysis shows clearly that a minor deviation of the radius can lead to irregularities / discontinuities of the contact pressure.

5 2: FE modelling and analysis of a steel spring The second case is related to a special steel spring which had to be investigated aiming to clarify a possible design failure. The device, used for mounting of light bulbs in lorries (Fig. 5), had cracking problems which were observed several times, indicating that the reason must be some mechanical overloading during mounting or loading. Fig. 6 shows the geometry of the spring which has a thickness much less than 1 mm. Its right side end is pushed down about 5 6 mm during mounting of the bulb, i.e. highly nonlinear. Another non-linearity is involved with the self contact of the folded part at left hand side. Figure 5: The steel spring in the mounted position before the additional loading by the light bulb. Due to the fact that self contact should be allowed properly, solids have been preferred instead of shells as element type. A FE model of hexahedron elements has been used for the half of the spring geometry taking the symmetry into account for the boundary conditions. In a first load step the fixation of the spring has been simulated. This has shown that the stresses can locally reach extreme values beyond the elastic limit. The superposition of the operational load, acting through the contact with the bulb, indicated then clearly that the stress concentrations were clearly underestimated in the design process.

6 Figure 6: The spring body consisting of highly flexible steel. Figure 7: The spring body undergoing self-contact and large displacements upon loading by the light bulb.

7 Figure 8: Remarkable deformation already due to mounting conditions. Figure 9: Stress concentrations beyond the allowable due to fastening of the slot at the upper part.

8 Figure 10: The spring body exhibits self-contact at its back side upon loading by the light bulb. The maximum principal stress reaches thereby high values exactly at the same position where cracks were observed occasionally. 3: Discussion / Conclusions The focus of the paper presented here was to point out that any optimisation attempt begins with the understanding of the current situation with all its problematic aspects. FE models, kept as simple as possible, but built and analysed as complete as necessary, are indispensable for its illustration and for a rather straight forward and efficient redesign process. Sensitivity considerations should be evaluated also carefully before deciding how to modify the product. In general, there are many ways or several parameters guiding to the same solution. In the latter case above, e.g., one can vary the fillet, the ligament or the thickness of the spring. Some useful hints about adequate FE modelling can be found in [1], a book dedicated to the basics in the practical application of the finite element method. REFERENCES [1] Deger, Y Methode der Finiten Elemente, 4 th Ed., Expert Verlag, Renningen, Germany, 2006.