When considering industrial models for aircraft braking systems, the number of degrees of freedom (DoF) limits the type of analysis that can be performed, an example being transient analyses. It is possible to reduce the number of DoF by simplifying the model through hypotheses. However this can affect the accuracy of the model, in particular its capacity to appropriately represent instabilities due to friction-induced vibrations. This paper assesses how the rigidity hypothesis, more specifically located at the rotor/stator components, can affect the precision of the model by comparing it to the non-rigid model and to experimental data. It will also provide an alternative model using reduction techniques. This paper investigates and discusses the hypothesis of non-deformation of the disks (i.e. rotors and stators in frictional contact) on the stability of an aircraft braking system at low frequencies. In order to conduct such a study, results based on finite element models considering rigid and non-rigid disks are compared. The non-rigid disk model is introduced and its performance is analysed in order to assess the improvement of the instability prediction. Then a model reduction technique is implemented in order to obtain a non-rigid model with a lower number of DoF. The performance of this new model is assessed with regard to the non-reduced model and to the rigid disks model. The model reduction appears to be very efficient in order to reproduce the eigemodes and eigenfrequencies predicted by the non-reduced model, while also keeping the DoF number as low as the rigid model. Besides, this method gives results which are closer to the experimental data, which indicates that the deformation of the disks plays a role on the whirl instability. More specifically it is observed that taking into account flexible rotor/stator disks provides a better prediction of the whirl frequency. The results linked to eigenmodes are related to a stability study : this requires to linearise the system around a sliding static equilibrium point. Hence, some conclusions would require to be validated for non-linear simulations and the prediction of friction-induced vibrations. Besides, the choice of the number and the distribution of the contact points has an influence on the results : it was small with respect to the magnitude of the error obtained throughout the study, but that might not be case in other situations. This paper adapts existing techniques to an industrial context and towards the prediction of a specific instability. This requires to take into account FE limitations and the frequency range of the instability. Besides, the models obtained through this process are compared to experimental data, in order to assess both model-to-model and model-to-data precision. An industrial challenge has been tackled here : how can we minimise the number of DoF while ensuring a satisfying precision when dealing with friction-induced instabilities ? This issue is shown for an aircraft braking system. Thanks to a model reduction technique, the model is validated by Complex Eigenvalue Analysis and can be used for transient simulation. This may be done in order to verify to which extent the results obtained here can be applied to the non-linear system.

Mr. Xavier Fagan, PhD student, Safran Landing Systems; Dr. Jean-Jacques Sinou, Professor, Laboratoire de Tribologie et Dynamique des Systèmes; Dr. Sébastien Besset, Professor, Laboratoire de Tribologie et Dynamique des Systèmes; Dr. Abdelbasset Hamdi, Methods specialist, Safran Landing Systems; Dr. Louis Jézéquel, Professor, Laboratoire de Tribologie et Dynamique des Systèmes