You are here : Version anglaise
-
Partager cette page
Lucien CHARROYER: Numerical methods for calculating self-sustaining friction-related vibrations: Application to railway squeal noise
Thesis submitted on December 19, 2017
Currently on permanent contract with ESI Group
Abstract:
This work is part of research intended to mitigate or eliminate the squeal noise produced by railway vehicles in curves or during braking. For instance, brake noise can reach very high sound levels up to 105 dB(A) close to the trains and constitutes an important nuisance for passengers and residents in the station. In order to provide some mitigation measures, the study focuses on the modelling of self-sustained structural vibrations in presence of frictional contact and the understanding of the squeal generation mechanism, especially for of a railway disc brake. It is assumed that vibration is due to structural mode coupling in the normal and tangential directions at the frictional interface. This coupling leads to instability of the sliding quasistatic equilibrium of the system and the occurrence of self-sustained vibrations. Two steps are necessary to calculate these vibrations. Firstly, the occurrence of the vibrations is determined through the stability analysis of the quasi-static equilibrium. In this thesis, two modelling assumptions for the friction law – planar or rectilinear – are compared in the case of an academic model. Without damping, the simplified rectilinear friction law tends to stabilize the system. With damping, the results established in the literature in case of rectilinear friction, especially the destabilization paradox, cannot be applied generally in case of planar friction even if similarities may be observed. Secondly, a nonlinear analysis is necessary and performed to calculate the amplitudes and the detailed spectral content of the self-sustained vibrations. This step is generally performed by using numerical time integration from given initial conditions, close to the equilibrium. Taking a look at the vibrations time histories obtained by this technique, two different states may be distinguished. In the transient state, nonlinear forces appear and gradually stabilize the unstable solution whereas in the steady (stationary) state, vibrations are stabilized. In the case of the academic model, the cause of the stabilization is highlighted thanks to a rigorous analysis of energy exchanges, especially the decrease of the power rate injected via the contact interface resulting from the accumulation of strongly nonlinear events like loss of contact, stick or impacts. However, direct time integration is not very appropriate in the case of large numerical models with many degrees of freedom. Indeed, the additional computational cost due to the transient state is very high although the determination of the steady state is generally sufficient from a practical point of view. Consequently, a method is proposed in order to directly approximate the steady state in case of mono-instability. This method combines a shooting technique with an initialization based on the above energy considerations. It is first validated on the minimal model and then transposed to the finite element model of a railway disc brake through an original approximation of the shooting technique : the reduction of the initial conditions phase space. The estimations of the steady states are compared with those obtained by direct time integration. The advantages and the limitations of the method are discussed.
This work is part of research intended to mitigate or eliminate the squeal noise produced by railway vehicles in curves or during braking. For instance, brake noise can reach very high sound levels up to 105 dB(A) close to the trains and constitutes an important nuisance for passengers and residents in the station. In order to provide some mitigation measures, the study focuses on the modelling of self-sustained structural vibrations in presence of frictional contact and the understanding of the squeal generation mechanism, especially for of a railway disc brake. It is assumed that vibration is due to structural mode coupling in the normal and tangential directions at the frictional interface. This coupling leads to instability of the sliding quasistatic equilibrium of the system and the occurrence of self-sustained vibrations. Two steps are necessary to calculate these vibrations. Firstly, the occurrence of the vibrations is determined through the stability analysis of the quasi-static equilibrium. In this thesis, two modelling assumptions for the friction law – planar or rectilinear – are compared in the case of an academic model. Without damping, the simplified rectilinear friction law tends to stabilize the system. With damping, the results established in the literature in case of rectilinear friction, especially the destabilization paradox, cannot be applied generally in case of planar friction even if similarities may be observed. Secondly, a nonlinear analysis is necessary and performed to calculate the amplitudes and the detailed spectral content of the self-sustained vibrations. This step is generally performed by using numerical time integration from given initial conditions, close to the equilibrium. Taking a look at the vibrations time histories obtained by this technique, two different states may be distinguished. In the transient state, nonlinear forces appear and gradually stabilize the unstable solution whereas in the steady (stationary) state, vibrations are stabilized. In the case of the academic model, the cause of the stabilization is highlighted thanks to a rigorous analysis of energy exchanges, especially the decrease of the power rate injected via the contact interface resulting from the accumulation of strongly nonlinear events like loss of contact, stick or impacts. However, direct time integration is not very appropriate in the case of large numerical models with many degrees of freedom. Indeed, the additional computational cost due to the transient state is very high although the determination of the steady state is generally sufficient from a practical point of view. Consequently, a method is proposed in order to directly approximate the steady state in case of mono-instability. This method combines a shooting technique with an initialization based on the above energy considerations. It is first validated on the minimal model and then transposed to the finite element model of a railway disc brake through an original approximation of the shooting technique : the reduction of the initial conditions phase space. The estimations of the steady states are compared with those obtained by direct time integration. The advantages and the limitations of the method are discussed.
