**2009-07-01 - Travail avec promoteur/Doctorat**- Français - 326 page(s)

Wattiaux David , "Simulation des niveaux vibratoires générés par les chocs pyrotechniques en vue de prédire les dysfonctionnements électriques des équipements embarqués"

**Codes CREF :**Sciences de l'ingénieur (DI2000), Mécanique (DI1240), Mécanique appliquée générale (DI2100), Mécanique appliquée spéciale (DI2200), Mécanique analytique ou rationnelle (DI1242), Technologie spatiale (DI2645)

**Texte intégral :**

- 2009_DW_Thesis.pdf (POSTPRINT,public)

**Abstract(s) :**

(Anglais) During their operational life, the electronic equipments embarked inside space shuttles may be exposed to severe vibratory environments often produced by the activation of pyrotechnic devices. Consequently, some failures in electronic and magnetic components may appear, as for example the loss of contact of electromagnetic relays or the appearance of cracks in the ferrite cores. In order to ensure the good working of the embarked material, it is essential to be able to reproduce, in laboratory, the vibratory environments which they will undergo during the different stages of the space flight. Thales Alenia Space ETCA industry, located at Charleroi (Belgium), has been developing for several years test facilities dedicated to check the pyroshock resistance of the electronic units (Figure 1). The pyroshock test facilities are classically resonant fixtures made up of an assembly of plates which is suspended to a tubular structure. The equivalence criteria used to specify a pyrotechnic vibratory environment are usually defined in terms of the Shock Response Spectrum (SRS). A new qualification campaign systematically begins by a trial/error process intended to update the significant parameters of the pyroshock test facility: location of the explosive charge, intensity of the impact, type of the test fixture (steel or aluminium plates), interface between plates, location of the equipment on the test facility,…When the vibratory levels, specified by the SRS specifications, are achieved, the nominal tests can be performed on the real electronic unit. Obviously, such a procedure can quickly become inefficient and expensive. This Ph.D. thesis develops, numerical tools allowing the prediction of the vibration levels generated by pyrotechnic shocks and the simulation of the dynamic behaviour of embarked electronic units subjected to external mechanical vibrations. Less costly, the modelling allows simulating the dynamic response of the system, in order to study the influence of the relevant operating parameters of the test facility and, in this way, to orientate the experimental procedure of the pyroshock testing. The computer modelling of pyroshocks requires an accurate dynamic model of the test facility as well as an accurate mathematical description of the excitation sources. For a pyroshock, the excitation sources are unknown because they cannot be directly measured. Consequently, they must be determined by an inverse method using a Finite Element model of the system and experimental measurements. The Finite Element Method (FEM) is used to model the dynamic behaviour of the structure. The FEM models of various configurations of the pyroshock test facility have been updated and validated up to 1000 Hz by comparing the modal properties, deduced from the FEM, with the ones experimentally identified from a modal analysis. Mode shapes at higher frequencies are much more difficult to identify due to the high modal density. Nevertheless we have assumed that it can be extrapolated at higher frequencies looking after to choose judiciously the element size. In practice, the vibration levels caused by mid-field pyroshocks, characterized by acceleration levels smaller than 5000 g and frequency range up to about 10 kHz, can be reproduced in laboratory by conventional impact devices such as pneumatic actuator or sledge hammer. These experimental observations motivated us to simulate the vibrations level generated by an explosive charge in replacing the actual excitation by an Equivalent Mechanical Shock (EMS). The EMS corresponds to a triangular impulse that has to be applied at the centre of the explosive device to generate an equivalent acceleration field. The main originality of this approach is to identify the amplitude and duration of the EMS by minimizing, using a least squares optimization process, the gap between the experimental and numerical results in terms of the SRS related to several points of the facility. Although our EMS approach is based on the hypothesis of a punctual and unidirectional excitation force, it leads to a good agreement between experimental and numerical SRS for all the points considered to identify the EMS; the mean difference is smaller than 3 dB (Figure 2). Besides, the impulse injected by the EMS is well correlated with the amount of explosive. Moreover, the EMS identified on one structure for a given amount of explosive, leads to coherent responses when it is applied on other structures. The encouraging results that we have obtained with the EMS approach lead us to investigate more sophisticated inverse methods, also based on punctual and unidirectional excitation force, to identify the excitation sources generated by an explosive charge. The inverse methods consist in identifying the time history of external forces applied to a mechanical structure from measured structural responses as far as an accurate model of its dynamic behaviour is available. In the framework of this Ph.D. thesis, we have envisaged two inverse methods using the deconvolution theory. The first one is based on the Wiener's filters theory and consists in building in the frequency domain an estimator of the unknown excitation sources. The second one consists in decomposing in the time domain the unknown force as a finite weighted sum of wavelets. These two methods assume that the excitation sources can be described by an unidirectional impact, localized at centre of the explosive device. Of course, in the case of pyroshock identification, these assumptions are open to criticism but they allow simplifying the mathematical developments. The advantage of the Wiener's filters method is that it establishes an one-to-one relation between the frequency components. Its weakness is that the destructive interferences of the reflecting waves can cause an ill-conditioning at certain frequencies (anti-resonance peaks). Besides, the Wiener's filters method is especially dedicated to the identification of stationary process. The wavelets deconvolution overcomes some disadvantages of the frequency domain. Firstly, it allows a better representation of the wave propagation in the structure (multiple reflexions). Secondly, it gives the possibility to limit the duration of the force, what is interesting for the identification of impulse loads. Therefore, time domain is better appropriate to the identification of transient processes than the frequency domain. Both methods behave properly for the identification of hammer impacts despite the fact that the Wiener’s method is principally dedicated to stationary processes. But, in the case of pyroshocks, both methods seem to be unable to properly identify the profile of a localized force equivalent to a pyroshock. The identified profiles are systematically undervalued on the whole of the frequency range, in particular for the Wiener's method which leads to mean differences larger than 9 dB between experimental SRS and the ones calculated from the transient dynamic response simulated by applying the identified force to the Finite Element model. The wavelet deconvolution method provides better results: it allows to estimate the characteristics of the shock (amplitude and duration) and to reproduce in the frequency range [1 ? 10 kHz] the vibration levels with accuracy comparable to the tolerances of the pyroshock specifications. At present time, the approach by Equivalent Mechanical Shock seems be the most appropriate tool to simulate an explosive charge in the case of the pyroshock test facility developed by Thales Alenia Space ETCA because the mean difference between experimental and simulated SRS is smaller than tolerances commonly admitted by pyroshock specifications. However, this approach doesn’t take into account the propagation of the pressure wave at the surface of the structure. Moreover, it is less general than the classical inverse methods because it requires imposing the force profile. Nevertheless, the EMS methodology can be exploited by the Thales Alenia Space ETCA industry during the qualification period to estimate the optimal parameters of the pyroshock test facility. At the same time to the identification of the pyrotechnic excitation sources, this research work takes also an active interest in the analysis of the sensitivity to shocks and vibrations of electromechanical relays (EMR). We have developed a simplified multiphysics model allowing predicting the limit vibration level that an EMR can undergo before a loss of contact appears. We have taken into account in our model mechanical aspects as well as magnetic aspects. The interaction between mechanical and magnetic phenomena has been described using an iterative technique based on the hypothesis of weak electromagnetic coupling. In our approach, the dynamic behaviour of the movable part of the ERM is represented by a cantilever beam. The resultant of the contact forces between the movable and static parts of the relay is taken in consideration by introducing a linear spring at the free end of the beam. The order of magnitude of the linear contact stiffness has been estimated using the Hertz’s theory and updated from the modal properties of the movable part identified when the relay is in the closed configuration. Concerning the damping effects, we have introduced in our model a stiffness and mass proportional damping whose the Rayleigh’s parameters ? and ? have been calculated from the identification of the damping ratio of the two first natural modes of the movable part. The magnetic force acting on the movable part of the relay has been computed using an equivalent magnetic circuit (Ampere’s law) for which the physical and geometrical properties have been experimentally identified. The contact is declared open as soon as the contact force becomes larger than the magnetic force. We have applied and validated our methodology to two study cases: non-latching PED PXC-1203 relay, used in classical industrial applications, and the latching GP250 relay which is commonly used inside electronic boxes of Ariane 5 launcher. In the case the PXC-1203 relay, the numerical predictions of the magnetic force have been compared, for several values of the rated voltage of the coil, with the ones obtained from 2D Finite Element predictions. The two numerical approaches provide similar results and allow reproducing in a satisfactory way the experimental measurements of this magnetic force. The methodology has been also validated by comparing, for harmonic excitations from 2 kHz to 8 kHz, the limit acceleration levels leading to a loss contact with the ones experimentally estimated (Figure 3). Besides, in the case of half-sinus shocks, our numerical predictions are coherent with the specifications given by the datasheet provided by the manufacturer. In the case of the GP250 relay, have shown that, for mechanical shocks as well as pyroshocks, the numerical predictions of the acceleration limit coincide with the orders of magnitude measured by Thales Alenia Space (branch of Toulouse). This Ph.D. thesis has mainly emphasized that a mathematical description of the excitation sources by an equivalent punctual force allows simulating the pyrotechnic vibratory environments with a reasonable accuracy as far as a series of precautions is respected such as the choice of the element size or the correction of the zeroshift. Besides, we have also elaborated a methodology allowing checking by simulation the resistance to vibrations and shocks of electromagnetic relays.