In the present work, an introduction to the contact phenomena in multibody systems is made. The different existing approaches are described, together with their most distinctive features. Then, the term of coefficient of restitution is emphasized as a tool to characterize impact events and the algorithm for calculating the relative indentation between two convex-shaped bodies is developed. Subsequently, the main penalty contact models developed in the last decades are presented and developed, analysing their advantages and drawbacks, as well as their respective applications. Furthermore, some models with specific peculiarities that could be useful to the reader are included. The aim of this work is to provide a resource to the novice researcher in the field to facilitate the choice of the appropriate contact model for their work.

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Maintenance is essential to prevent catastrophic failures in rotating machinery. A crack can cause a failure with costly processes of reparation, especially in a rotating shaft.In this study, the wavelet transform theory was applied to vibration signals to detect cracks in a rotating shaft. Data were obtained from an analytical Jeffcott rotor model with a breathing function to simulate cracks. Large changes in energy when a crack appears were discovered at 1x, 2x and 3x. Thereafter, vibration signals were obtained from a rotating machine at different steady-state rotational speeds using an accelerometer mounted on the bearing housing. Nine defect conditions were induced in the shaft (with depths from 4% to 50% of the shaft diameter). By matching the theoretical results with the experimental data, it was found that only the 3x component of the rotational speed is a clear indicator of the presence of a crack in this case. The energy level at this harmonic can be used for the inverse process of crack detection. Moreover, "probability of detection" curves were calculated. They showed very good results.

An efficient maintenance is a key consideration in systems of railway transport, especially in high-speed trains, in order to avoid accidents with catastrophic consequences. In this sense, having a method that allows for the early detection of defects in critical elements, such as the bogie mechanical components, is a crucial for increasing the availability of rolling stock and reducing maintenance costs. The main contribution of this work is the proposal of a methodology that, based on classical signal processing techniques, provides a set of parameters for the fast identification of the operating state of a critical mechanical system. With this methodology, the vibratory behaviour of a very complex mechanical system is characterised, through variable inputs, which will allow for the detection of possible changes in the mechanical elements. This methodology is applied to a real high-speed train in commercial service, with the aim of studying the vibratory behaviour of the train (specifically, the bogie) before and after a maintenance operation. The results obtained with this methodology demonstrated the usefulness of the new procedure and allowed for the disclosure of reductions between 15% and 45% in the spectral power of selected Intrinsic Mode Functions (IMFs) after the maintenance operation.

This work presents and discusses a general approach for the dynamic modeling and analysis of a passive biped walking robot, with a particular focus on the feet-ground contact interaction. The main purpose of this investigation is to address the supporting foot slippage and viscoelastic dissipative contact forces of the biped robot-walking model and to develop its dynamics equations for simple and double support phases. For this investigation, special attention has been given to the detection of the contact/impact between the legs of the biped and the ground. The results have been obtained with multibody system dynamics applying forward dynamics. This study aims at examining and comparing several force models dealing with different approaches in the context of multibody system dynamics. The normal contact forces developed during the dynamic walking of the robot are evaluated using several models: Hertz, Kelvin-Voight, Hunt and Crossley, Lankarani and Nikravesh, and Flores. Thanks to this comparison, it was shown that the normal force that works best for this model is the dissipative Nonlinear Flores Contact Force Model (hysteresis damping parameter - energy dissipation). Likewise, the friction contact/impact problem is solved using the Bengisu equations. The numerical results reveal that the stable periodic solutions are robust. Integrators and resolution methods are also purchased, in order to obtain the most efficient ones for this model.