Modelisation of thermoelastic linear behaviour of tungsten filaments in simple and twin helical spring configurations

By trying to increase the luminosity or the life expectancy of an incandescent lamp, an idea consists of a series of successive rolling up of the tungsten filament. This gives geometrical configurations of filaments named simple, twin, or triple helical spring, etc… In this paper, we will limit only to the cases of the simple and twin helical spring filaments. Under the combined effects of the high temperature and the stresses induced by its own weight, the filament creeps by becoming plastically deformed in a permanent and a continuously manner, until the rupture. The theoretical study of the behaviour of these filaments needs the knowledge of internal efforts distribution, deformations modes, and their evolutions. The present work consists on an elastic structural analysis which must be the first step. Since the objective is also to study the influence of the filament self-weight solicitation, the orientation (or position) with respect to gravitational direction should be taken into account. Numerical results are obtained by finite element method. They showed a negligible influence of the solicitations due to the variation of the temperature with respect to those of the self-weight, and a relative sensitivity to the position changes for the twin helical spring filament. For this later, we have developed an analytical method which is only valid in the case of a vertical position. Because of some difficulties, the comparison between the numerical and analytical results could not be carried out directly. However, the analytical approach proved to be qualitatively useful for the analysis of numerical results.