The destabilization paradox applied to friction-induced vibrations in an aircraft braking system

Abstract

Mechanisms of friction are known as an important source of vibrations in a large variety of engineering systems, where the emergence of oscillations is noisy and can cause severe damage to the system. The reduction or elimination of these vibrations is then an industrial issue that requires the attention of engineers and researchers together. Friction-induced vibrations have been the matter of several investigations, considering experimental, analytical, and numerical approaches. An aircraft braking system is a complex engineering system prone to friction-induced vibrations, and is the subject herein. By considering experimental observations and by evaluating the mechanisms of friction involved, a complete nonlinear model is built. The nonlinear contact between the rotors and the stators is considered. The stability analysis is performed by determining the eigenvalues of the linearized system at the equilibrium point. Parametric studies are conducted in order to evaluate the effects of various system parameters on stability. Special attention will be given to the understanding the role of damping and the associated destabilization paradox in mode-coupling instabilities.

Nonlinear transient vibrations and coexistences of multi-instabilities induced by friction in an aircraft braking system

“…A reduced number of degrees of freedom is a susbstantial advantage for the full temporal integration of the dynamical equations. This model has already been used by Chevillot et al [14] to study the effects of damping on stability.…”

“…(2) and (3)), the global expression of the nonlinear terms F NL can be expressed. The latter have been presented in a previous study [14] and are developed in Appendix A. After calculation, the nonlinear equations of motions can be written in the following form [14]:…”

“…4(a) and (b). No structural damping is added for this calculation (for more details about the effects of damping on stability see [14,25,26,27,28,29]). Five instabilities are calculated between 0 and 800 Hz, corresponding to the frequency range in which the analytical model is assumed to be efficient.…”

“…Studies on whirl, another kind of friction-induced instability in aircraft brakes, were first performed by Travis [10] and Hagler [11], and completed by the work of Sinou et al [12,13] by using geometric coupling and sprag-slip approaches. Finally, a complete nonlinear approach for whirl and squeal instabilities has been presented by Chevillot et al [14].…”

Untwisting the Campbell diagrams of weakly anisotropic rotor systems

“…In the latter supercritical flutter and divergence instabilities are easily excited just by the Hamiltonian perturbations like stiffness modification near the crossings with the mixed Krein signature. Among the low-speed applications the untwisting of the Campbell diagram is directly related to the onset of friction-induced oscillations in brakes, clutches, paper calenders, and even in musical instruments like the glass harmonica [9,44,45,46,47,48,51]. In contrast to the supercritical instabilities, the excitation of the subcritical flutter near the crossings with the definite Krein signature by the Hamiltonian perturbations only, is impossible.…”