Non-Linear Dynamics of a Complex Aircraft Brake System: Experimental and Theoretical Approaches

Abstract

Stability and non-linear dynamics in a complex aircraft brake model are investigated. The non-linear contact between the rotors ands the stators, and mechanisms between components of the brake system are considered. The stability analysis is performed by determining the eigenvalues of the jacobian matrix of the linearized system at the equilibrium point. Parametric studies with linear stability theory is conducted in order to determine the effect of system parameters on stability. In order to obtain time-history responses, the complete set of nonlinear dynamic equations may be integrated numerically. But this procedure is both time consuming and costly to perform when parametric design studies are needed. So it is necessary to use nonlinear analysis : the center manifold approach and the rational approximants are used to obtain the limit cycle of the non-linear system and to study the behaviour of the system in the unstable region. Results from these nonlinear methods are compared with results obtained by integrating the full original system. These non-linear methods appear very interesting in regard to computational time and also necessitate very few computer resources.

Stability analysis and non-linear behaviour of structural systems using the complex non-linear modal analysis (CNLMA)

“…4 illustrates the evolution of the two coupling unstable modes for l 2 0:32 0:81 ½ . The unstable mode occurs at 250 Hz that indicates a perfect correlation with experimental tests [35]. Finally, Fig.…”

“…2: industry experience [35] has identified an important specific unstable vibration mode called whirl. Experimental approaches and laboratory vibrational tests that represent the aircraft operating environment indicate that the consequences of this whirl instability due to friction-induced vibration can be drastic and cause large amplitude oscillations of the aircraft brake system components.…”

“…Considering static tests [35], it has been observed that the normal contact N(r, h) at the rotor-stator interface can be represented by a cubic polynomial in the relative displacement between the rotor and stator in compression…”

Methods to reduce non-linear mechanical systems for instability computation

“…where v c = {v c1 v c2 } T , and f NL is the vector of the SOD approximants in (v c1 , v c2 ). Then, the Alternate Frequency/Time domain method is based upon assumptions about a Fourier expansion for the non-linear response of the non-linear system (168). We assume that the vector solution v c = {v c1 v c2 } T can be expanded as a truncated Fourier series:…”

“…The aim of this section is to provide an introduction to Padé approximations and the general rational fractional approximants in 2-variables that will be applied after the centre manifold analysis. In many branches of engineering sciences, Padé approximants and rational fractional approximants have found numerous applications ( [40], [35], [36], [201], [200], [55], [155], [170], [169], [168] and [175]); the solution of a given problem in applied sciences is often described as a power series expansion. In this case, one of the interesting aims is to approximate the function from its series expansion.…”